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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.