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Publikationen - Journal Articles
Blanc, Jérémy: Conjugacy classes of special automorphisms of the affine spaces, in:
Algebra Number Theory 10, 2016, H. 5, S. 939-967.Blanc, Jérémy: Conjugacy classes
of special automorphisms of the affine spaces, , 2016In the group of polynomial
automorphisms of the plane, the conjugacy class of an element is closed if and only if
the element is diagonalisable. In this article, we show that this does not hold for the
group of special automorphisms, giving then a first step towards the direction of
showing that this group is not simple, as an infinite- dimensional algebraic group.
(Abriss)
Blanc, Jérémy: Algebraic elements of the Cremona groups, in: Proceedings of the
conference "Hommage to Corrado Segre" , 2016, S. to appear.Blanc, Jérémy:
Algebraic elements of the Cremona groups, , 2016This article studies algebraic
elements of the Cremona group. In particular, we show that the set of all these elements
is a countable union of closed subsets but it not closed. (Abriss)
Blanc, Jeremy; Calabri, Alberto: On degenerations of plane Cremona transformations,
in: Mathematische Zeitschrift 282, 2016, H. 1-2, S. 223-245.Blanc, Jeremy; Calabri,
Alberto: On degenerations of plane Cremona transformations, , 2016This article
studies the possible degenerations of Cremona transforma- tions of the plane of some
degree into maps of smaller degree. (Abriss)
Blanc, Jeremy; Cantat, Serge: Dynamical degrees of birational transformations of
projective surfaces, in: Journal of the American Mathematical Society (JAMS) 29, 2016,
H. 2, S. 415-471.Blanc, Jeremy; Cantat, Serge: Dynamical degrees of birational
transformations of projective surfaces, , 2016The dynamical degree lambda( f ) of a
birational transformation f measures the exponential growth rate of the degree of the
formulae that define the n -th iterate of f . We study the set of all dynamical degrees of
all birational transformations of projective surfaces, and the relationship between the
value of lambda( f ) and the structure of the conjugacy class of f . For instance, the set
of all dynamical degrees of birational transformations of the complex projective plane is
a closed and well ordered set of algebraic numbers. (Abriss)
Blanc, Jeremy; Furter, Jean-Philippe; Poloni, Pierre-Marie: Extension of automorphisms
of rational smooth affine curves, in: Mathematical research letters 23, 2016, H. 1, S.
43-66.Blanc, Jeremy; Furter, Jean-Philippe; Poloni, Pierre-Marie: Extension of
automorphisms of rational smooth affine curves, , 2016We provide the existence, for
every complex rational smooth affine curve Γ, of a linear action of Aut(Γ) on the affine
3-dimensional space A3, together with a Aut(Γ)-equivariant closed embedding of Γ into
A3. It is not possible to decrease the dimension of the target, the reason for this obstruction is also precisely described. (Abriss)
Blanc, Jérémy; Zimmermann, Susanna: Topological simplicity of the Cremona groups,
in: Amer. Journal of Math. , 2016, S. (to appear).Blanc, Jérémy; Zimmermann,
Susanna: Topological simplicity of the Cremona groups, , 2016The Cremona group is
topologically simple when endowed with the Zariski or Euclidean topology, in any
dimension ≥ 2 and over any infinite field. Two elements are moreover always connected
by an affine line, so the group is path-connected. (Abriss)
Blanc, Jérémy: Non-rationality of some fibrations associated to Klein surfaces, in:
Beiträge zur Algebra und Geometrie 56, 2015, H. 1, S. 351-371.Blanc, Jérémy:
Non-rationality of some fibrations associated to Klein surfaces, , 2015We study the
polynomial fibration induced by the equation of theKlein surfaces obtained as quotient of
finite linear groups of automorphisms ofthe plane; this surfaces are of type A, D, E,
corresponding to their singularities.The generic fibre of the polynomial fibration is a
surface defined over thefunction field of the line. We proved that it is not rational in
cases D, E,although it is obviously rational in the case A.The group of automorphisms of
the Klein surfaces is also described, and islinear and of finite dimension in cases D, E;
this result being obviously falsein case A. (Abriss / )
Blanc, Jeremy; Canci, Jung Kyu; Elkies, Noam D.: Moduli spaces of quadratic rational
maps with a marked periodic point of small order, in: International mathematics
research notices 2015, 2015, H. 23, S. 12459-12489.Blanc, Jeremy; Canci, Jung Kyu;
Elkies, Noam D.: Moduli spaces of quadratic rational maps with a marked periodic
point of small order, , 2015The surface corresponding to the moduli space of quadratic
endomorphisms of P1 with a marked periodic point of order n is studied. It is shown that
the surface is rational over Q when n 5 and is of general type for n = 6. An explicit
description of the n = 6 surface lets us find several infinite families of quadratic
endomorphisms f : P1-> P1 defined over Q with a rational periodic point of order 6. In
one of these families, f also has a rational fixed point, for a total of at least 7 periodic
and 7 preperiodic points. This is in contrast with the polynomial case, where it is
conjectured that no polynomial endomorphism defined over Q admits rational periodic
points of order n > 3. (Abriss / )
Blanc, Jeremy; Deserti, Julie: Degree growth of birational maps of the plane, in: Annali
della Scuola Normale di Pisa - Classe di Scienze 14, 2015, H. 2, S. 507-533.Blanc,
Jeremy; Deserti, Julie: Degree growth of birational maps of the plane, , 2015This
article studies the sequence of iterative degrees of a birational map of the plane. This
sequence is known either to be bounded or to have a linear, quadratic or exponential
growth. The classification elements of infinite order with a bounded sequence of
degrees is achieved, the case of elements of finite order being already known. The
coefficients of the linear and quadratic growth are then described, and related to
geometrical properties of the map. The dynamical number of base-points is also
studied. Applications of our results are the description of embeddings of the
Baumslag-Solitar groups and GL(2,Q) into the Cremona group. (Abriss)
Blanc, Jeremy; Dolgachev, Igor: Automorphisms of cluster algebras of rank 2, in:
Transformation groups 20, 2015, H. 1, S. 1-20.Blanc, Jeremy; Dolgachev, Igor:
Automorphisms of cluster algebras of rank 2, , 2015We compute the automorphism
group of the affine surfaces with the coor- dinate ring isomorphic to a cluster algebra of
rank 2. (Abriss / )
Blanc, Jeremy; Dubouloz, Adrien: Affine surfaces with a huge group of automorphisms,
in: International mathematics research notices 2015, 2015, H. 2, S. 422-459.Blanc,
Jeremy; Dubouloz, Adrien: Affine surfaces with a huge group of automorphisms, ,
2015We describe a family of rational affine surfaces S with huge groups of
automorphisms in the following sense: the normalsubgroup Aut(S)alg of Aut(S)
generated by all algebraic subgroups of Aut(S) is not generated by any countable
familyof such subgroups, and the quotient Aut(S)/Aut(S)alg cointains a free group over
an uncountable set of generators. (Abriss / )
Blanc, Jérémy; Hedén, Isac: The group of Cremona transformations generated by linear
maps and the standard involution, in: Annales de l'institut Fourier 65, 2015, H. 6, S.
2641-2680.Blanc, Jérémy; Hedén, Isac: The group of Cremona transformations
generated by linear maps and the standard involution, , 2015This article studies the
group generated by automorphisms of the projectivespace of dimension n and by the
standard birational involution of degree n .Every element of this group only contracts
rational hypersurfaces, but in odd dimension,there are simple elements having this
property which do not belong to the group.Geometric properties of the elements of the
group are given, as well as a descriptionof its intersection with monomial
transformations. (Abriss)
Blanc, Jérémy; Lamy, Stéphane: On birational maps from cubic threefolds, in:
North-Western European Journal of Mathematics 1, 2015, S. 55-84.Blanc, Jérémy;
Lamy, Stéphane: On birational maps from cubic threefolds, , 2015We characterise
smooth curves in a smooth cubic threefold whose blow-ups produce a weak-Fano
threefold. These are curves C of genus g and degree d, such that (i) 2(d −5) ≤ g and d ≤
6; (ii) C does not admit a 3-secant line in the cubic threefold. Among the list of ten
possible such types (g,d), two yield Sarkisov links that are birational selfmaps of the
cubic threefold, namely (g,d) = (0,5) and (2,6). Using the link associated with a curve of
type (2, 6), we are able to produce the first example of a pseudo-automorphism with
dynamical degree greater than 1 on a smooth threefold with Picard number 3. We also
prove that the group of birational selfmaps of any smooth cubic threefold contains
elements contracting surfaces birational to any given ruled surface. (Abriss / )
Blanc, Jérémy; Stampfli, Immanuel: Automorphisms of the plane preserving a curve, in:
Algebraic geometry 2, 2015, H. 2, S. 193-213.Blanc, Jérémy; Stampfli, Immanuel:
Automorphisms of the plane preserving a curve, , 2015We study the group of
automorphisms of the affine plane preserv- ing some given curve, over any field. The
group is proven to be algebraic, except in the case where the curve is a bunch of
parallel lines. Moreover, a classification of the groups of positive dimension occuring is
also given in the case where the curve is geometrically irreducible and the field is
perfect. (Abriss)
Blanc, Jeremy: Dynamical degrees of (pseudo)-automorphisms fixing cubic
hypersurfaces, in: Indiana University mathematics journal 62, 2013, H. 4, S.
1143-1164.Blanc, Jeremy: Dynamical degrees of (pseudo)-automorphisms fixing cubic
hypersurfaces, , 2013We give a way to construct group of pseudo-automorphisms
ofrational varieties of any dimension that fix pointwise the image of a cubichypersurface
of p^n. These group are free products of involutions, and most oftheir elements have
dynamical degree > 1. Moreover, the Picard group of thevarieties obtained is not big, if
the dimension is at least 3.We also answer a question of E. Bedford on the existence of
birational mapsof the plane that cannot be lifted to automorphisms of dynamical degree
> 1,even if we compose them with an automorphism of the plane. (Abriss / )
Blanc, Jeremy: Symplectic birational transformations of the plane, in: Osaka journal of
mathematics 50, 2013, H. 2, S. 573-590.Blanc, Jeremy: Symplectic birational
transformations of the plane, , 2013We study the group of symplectic birational
transformations ofthe plane. It is proved that this group is generated by SL(2; Z), the
torus anda special map of order 5, as it was conjectured by A. Usnich.Then we consider
a special subgroup H, of nite type, dened over anyeld which admits a surjective
morphism to the Thompson group of piecewiselinear automorphisms of Z2. We prove
that the presentation for this groupconjectured by Usnich is correct. (Abriss / )
Blanc, Jeremy; Furter, Jean-Philippe: Topologies and structures of the Cremona group,
in: Annals of mathematics. Series 2 178, 2013, H. 3, S. 1173-1198.Blanc, Jeremy;
Furter, Jean-Philippe: Topologies and structures of the Cremona group, , 2013We
study the algebraic structure of the n-dimensional Cremonagroup and show that it is not
an algebraic group of infinite dimension (indgroup)if n>1. We describe the obstruction to
this, which is of a topologicalnature.By contrast, we show the existence of a Euclidean
topology on the Cremonagroup which extends that of its classical subgroups and makes
it a topologicalgroup. (Abriss / )
Blanc, Jeremy: Simple relations in the Cremona group, in: Proceedings of the American
Mathematical Society 140, 2012, H. 5, S. 1495-1500.Blanc, Jeremy: Simple relations
in the Cremona group, , 2012We give a simple set of generators and relations for the
Cre-mona group of the plane. Namely, we show that the Cremona group is
theamalgamated product of the de Jonquieres group with the group of auto-morphisms
of the plane, divided by one relation . (Abriss / )
Blanc, Jeremy; Deserti, Julie: Embeddings of SL(2,Z) into the Cremona group, in:
Transformation groups 17, 2012, H. 1, S. 21-50.Blanc, Jeremy; Deserti, Julie:
Embeddings of SL(2,Z) into the Cremona group, , 2012Geometric and dynamic
properties of embeddings of SL(2;Z) into the Cremona group are studied. Infinitely
manynon-conjugate embeddings which preserve the type (i.e. which send elliptic,
parabolic and hyperbolic elements onto elements ofthe same type) are provided. The
existence of infinitely many non-conjugate elliptic, parabolic and hyperbolic embeddings
is alsoshown.In particular, a group G of automorphisms of a smooth surface S obtained
by blowing-up 10 points of the complex projectiveplane is given. The group G is
isomorphic to SL(2;Z), preserves an elliptic curve and all its elements of infinite order
are hyperbolic. (Abriss / )
Blanc, Jeremy; Lamy, Stephane: Weak Fano threefolds obtained by blowing-up a space
curve and construction of Sarkisov links, in: Proceedings of the London Mathematical
Society 105, 2012, H. 5, S. 1047-1075.Blanc, Jeremy; Lamy, Stephane: Weak Fano
threefolds obtained by blowing-up a space curve and construction of Sarkisov links, ,
2012We characterise smooth curves in P3 whose blow-up producesa threefold with
anticanonical divisor big and nef. These arecurves C of degree d and genus g lying on a
smooth quartic, such that(i) 4d - 30<= g<= 14 or (g; d) = (19; 12), (ii) there is no
5-secant line,9-secant conic, nor 13-secant twisted cubic to C. This generalises
theclassical similar situation for the blow-up of points in P2.We describe then Sarkisov
links constructed from these blow-ups, andare able to prove the existence of Sarkisov
links which were previouslyonly known as numerical possibilities. (Abriss / )
Blanc, Jeremy: Elements and cyclic subgroups of finite order of the Cremona group, in:
Commentarii mathematici Helvetici 86, 2011, H. 2, S. 469-497.Blanc, Jeremy:
Elements and cyclic subgroups of finite order of the Cremona group, , 2011We give
the classication of elements { respectively cyclic subgroups {of nite order of the
Cremona group, up to conjugation. Natural parametri-sations of conjugacy classes,
related to xed curves of positive genus, areprovided. (Abriss / )
Blanc, Jérémy: The best polynomial bounds for the number of triangles in a simple
arrangement of n pseudo-lines, in: Geombinatorics 21, 2011, H. 1, S. 5-14.Blanc,
Jérémy: The best polynomial bounds for the number of triangles in a simple
arrangement of n pseudo-lines, , 2011It is well-known and easy to observe that affine
(respectively projective)simple arrangement of n pseudo-lines may have at most n(n −
2)/3(respectively n(n − 1)/3) triangles. However, these bounds are reached foronly
some values of n (mod 6). We provide the best polynomial bound for theaffine and the
projective case, and for each value of n (mod 6). (Abriss)
Blanc, Jérémy; Dubouloz, Adrien: Automorphisms of A1-fibered affine surfaces, in:
Trans. Amer. Math. Soc. 363, 2011, H. 2011, S. 5887-5924.Blanc, Jérémy; Dubouloz,
Adrien: Automorphisms of A1-fibered affine surfaces, , 2011We develop technics of
birational geometry to study automorphisms of affine surfacesadmitting many distinct
rational fibrations, with a particular focus on the interactions between
automorphismsand these fibrations. In particular, we associate to each surface S of this
type a graphencoding equivalence classes of rational fibrations from which it is possible
to decide for instance if theautomorphism group of S is generated by automorphisms
preserving these fibrations. (Abriss)
Blanc, Jeremy; Mangolte, Frederic: Geometrically rational real conic bundles and very
transitive actions, in: Compositio mathematica 147, 2011, H. 1, S. 161-187.Blanc,
Jeremy; Mangolte, Frederic: Geometrically rational real conic bundles and very
transitive actions, , 2011In this article we study the transitivity of the group of
automorphisms of real algebraic sur- faces. We characterize real algebraic surfaces
with very transitive automorphism groups. We give applications to the classification of
real algebraic models of compact surfaces: these applications yield new insight into the
geometry of the real locus, proving several surprising facts on this geometry. This
geometry can be thought of as a half-way point between the biregular and birational
geometries. (Abriss)
Blanc, Jérémy: Groupes de Cremona, connexité et simplicité, in: Annales scientifiques
de l'école normale supérieure 43, 2010, H. 2, S. 357-364.Blanc, Jérémy: Groupes de
Cremona, connexité et simplicité, , 2010The Cremona group is connected in any
dimension and, endowedwith its topology, it is simple in dimension 2. (Abriss)
Blanc, Jeremy: Linearisation of finite Abelian subgroups of the Cremona group of the
plane, in: Groups, geometry and dynamics 3, 2009, H. 2, S. 215-266.Blanc, Jeremy:
Linearisation of finite Abelian subgroups of the Cremona group of the plane, ,
2009Given a finite Abelian subgroup of the Cremona group of the plane, weprovide a
way to decide whether it is birationally conjugate to a group ofautomorphisms of a
minimal surface.In particular, we prove that a finite cyclic group of birational
transformationsof the plane is linearisable if and only if none of its non-trivial elementsfix
a curve of positive genus. For finite Abelian groups, there exists only onesurprising
exception, a group isomorphic to Z/2Z xZ/4Z, whose non-trivialelements do not fix a
curve of positive genus but which is not conjugate toa group of automorphisms of a
minimal rational surface.We also give some descriptions of automorphisms (not
necessarily of finiteorder) of del Pezzo surfaces and conic bundles. (Abriss)
Blanc, Jeremy: Sous-groupes algébriques du groupe de Cremona, in: Transformation
groups 14, 2009, H. 2, S. 249-285.Blanc, Jeremy: Sous-groupes algébriques du
groupe de Cremona, , 2009We give a complete classification of maximal algebraic
subgroups of the Cremona group Bir(P2) and provide algebraic varieties that
parametrize the conjugacy classes. (Abriss)
Blanc, Jeremy: The correspondence between a plane curve and its complement, in:
Journal für die reine und angewandte Mathematik 633, 2009, S. 1-10.Blanc, Jeremy:
The correspondence between a plane curve and its complement, , 2009Given two
irreducible curves of the plane which have isomorphic complements, it is natural to ask
whether there exists an automorphism of the plane that sends one curve on the
other.This question has a positive answer for a large family of curves and H. Yoshihara conjectured that it is true in general. We exhibit counterexamples to this
conjecture, over any ground field. In some of the cases, the curves are isomor- phic and
in others not; this provides counterexamples of two different kinds.Finally, we use our
construction to find the existence of surprising non- linear automorphisms of affine
surfaces. (Abriss)
Blanc, Jeremy; Pan, Ivan; Vust, Thierry: On birational transformations of pairs in the
complex plane, in: Geometriae dedicata 139, 2009, H. 1, S. 57-73.Blanc, Jeremy; Pan,
Ivan; Vust, Thierry: On birational transformations of pairs in the complex plane, ,
2009This article deals with the study of the birational transformations of the projective
complex plane which leave invariant an irreducible algebraic curve. We try to describe
the state of the art and provide some new results on this subject. (Abriss)
Bartholdi, Nicolas; Blanc, Jérémy; Loisel, Sébastien: On simple arrangements of lines
and pseudo-lines in P2 and R2 with the maximal number of triangles, in: Contemporary
mathematics 453, 2008, S. 105-116.Bartholdi, Nicolas; Blanc, Jérémy; Loisel,
Sébastien: On simple arrangements of lines and pseudo-lines in P2 and R2 with the
maximal number of triangles, , 2008
Blanc, Jeremy: On the inertia group of elliptic curves in the Cremona group of the plane,
in: >>The 56, 2008, H. 2, S. 315-330.Blanc, Jeremy: On the inertia group of elliptic
curves in the Cremona group of the plane, , 2008We study the group of birational
transformations of the plane thatfix (each point of) a curve of geometric genus 1.A
precise description of the finite elements is given; it is shown in particularthat the order
is at most 6, and that if the group contains a non-trivial torsion,the fixed curve is the
image of a smooth cubic by a birational transformationof the plane.We show that for a
smooth cubic, the group is generated by its elementsof degree 3, and prove that it
contains a free product of Z/2Z, indexed by thepoints of the curve. (Abriss)
Blanc, Jeremy; Pan, Ivan; Vust, Thierry: Sur un théorème de Castelnuovo, in: Bulletin of
the Brazilian Mathematical Society 39, 2008, H. 1, S. 61-80.Blanc, Jeremy; Pan, Ivan;
Vust, Thierry: Sur un théorème de Castelnuovo, , 2008We continue the study of G.
Castelnuovo on the group of birationaltransformation of the complex plane that fix each
point of a curve of genus> 1 ; we use adjoint linear system of the curve as Castelnuovo
does.We prove that these groups are abelian, and that these are either finite, oforder 2
or 3, or conjuguate to a subgroup of the de Jonqui`eres group. We showalso that these
results do not generalise to curves of genus 1.Keywords. Cremona transformations,
birational transformations, fixed curves,curves of big genus, adjoint linear system, de
Jonqui`eres transformations. (Abriss)
Blanc, Jeremy: Finite Abelian subgroups of the Cremona group of the plane, in:
Comptes rendus de l'Académie des sciences. Série 1, Mathématique. Series 1,
Mathematics 344, 2007, H. 1, S. 21-26.Blanc, Jeremy: Finite Abelian subgroups of the
Cremona group of the plane, , 2007We present in this Note some results on conjugacy
classes of finite Abelian subgroups of the Cremona group of the plane. (Abriss)
Blanc, Jeremy: The number of conjugacy classes of elements of the Cremona group of
some given finite order, in: Bulletin de la Société mathématique de France 135, 2007,
H. 3, S. 419-434.Blanc, Jeremy: The number of conjugacy classes of elements of the
Cremona group of some given finite order, , 2007This note presents the study of the
conjugacy classes of elements ofsome given finite order n in the Cremona group of the
plane. In particular, it is shownthat the number of conjugacy classes is infinite if n is
even, n = 3 or n = 5, and that itis equal to 3 (respectively 9) if n = 9 (respectively if n =
15) and to 1 for all remainingodd orders.Some precise representative elements of the
classes are given. (Abriss)
Blanc, J: Conjugacy classes of affine automorphisms of Kn and linear automorphisms of
Pn in the Cremona groups, in: Manuscripta mathematica 119, 2006, H. 2, S.
225-241.Blanc, J: Conjugacy classes of affine automorphisms of Kn and linear
automorphisms of Pn in the Cremona groups, , 2006We describe the conjugacy
classes of affine automorphisms in the groupAut(n,K) (respectively Bir(Kn)) of
automorphisms (respectively of birationalmaps) of Kn. From this we deduce also the
classification of conjugacy classes ofautomorphisms of Pn in the Cremona group
Bir(Kn). (Abriss)
Beauville, A; Blanc, K: On Cremona transformations of prime order, in: Comptes rendus
de l'Académie des sciences. Série 1, Mathématique. Series 1, Mathematics 339, 2004,
H. 4, S. 257-259.Beauville, A; Blanc, K: On Cremona transformations of prime order,
, 2004We prove that an automorphism of order 5 of the Del Pezzo surface S5 of degree
5 is conjugate through abirational map S 99K P2 to a linear automorphism of P2. This
completes the classification of conjugacy classes ofelements of prime order in the
Cremona group. (Abriss)
Publikationen - Essays in Anthologies
Blanc, Jérémy: Algebraic structures of groups of birational transformations, in: Clifford
Lectures, New Orleans 2016. Blanc, Jérémy: Algebraic structures of groups of
birational transformations, 2016A priori, the set of birational transformations of an
algebraic va- riety is just a group. We survey the possible algebraic structures that we
may add to it, using in particular parametrised family of birational transformations.
(Abriss)
Blanc, Jérémy; Mangolte, Frédéric: Cremona groups of real surfaces, in:
Automorphisms in birational and affine geometry, Part 1, birational automorphisms, 19
S. Trento 2013 (= Part 1, birational automorphisms, 19 S.). Blanc, Jérémy; Mangolte,
Frédéric: Cremona groups of real surfaces, 2013We give an explicit set of generators
for various natural subgroups of the real Cremona group Bir(2). This completes and
unifies former results by several authors. (Abriss / )
Publikationen - Preprints
Blanc, Jérémy: Conjugacy classes of special automorphisms of the affine spaces, 2015.
Blanc, Jérémy: Algebraic structures of groups of birational transformations, 2015.