1736 - RIMS, Kyoto University
... (a) Assume that X is not of general type and that the Iitaka fibration X → C is not quasi-elliptic when the Kodaira dimension κ(X) is 1 and p = 2, 3. Then R.V. holds on X. (b) If R.V. does not hold on X, then there exist a birational morphism X ′ → X and a morphism g : X ′ → C onto a smooth algebraic ...
... (a) Assume that X is not of general type and that the Iitaka fibration X → C is not quasi-elliptic when the Kodaira dimension κ(X) is 1 and p = 2, 3. Then R.V. holds on X. (b) If R.V. does not hold on X, then there exist a birational morphism X ′ → X and a morphism g : X ′ → C onto a smooth algebraic ...
Sums of Fractions and Finiteness of Monodromy
... (λ, µ, ν) ∈ the finite list in Table 1 below. Remark. Again, though the statement of the theorem is purely (elementary) number theoretic, the proof uses the finiteness of a certain group Γ in GL2 (C). It would be interesting to find a purely number theoretic proof of the above theorem. 2.3. Relation ...
... (λ, µ, ν) ∈ the finite list in Table 1 below. Remark. Again, though the statement of the theorem is purely (elementary) number theoretic, the proof uses the finiteness of a certain group Γ in GL2 (C). It would be interesting to find a purely number theoretic proof of the above theorem. 2.3. Relation ...
What Does the Spectral Theorem Say?
... nor bounded operatorrepresentationsof functionalgebras,are in the daily toolkit of everyworkingmathematician.In contrast,the formulationof the spectral theoremgiven below uses only the relativelyelementaryconcepts of measure theory.This formulationhas been part of the oral traditionof Hilbert space ...
... nor bounded operatorrepresentationsof functionalgebras,are in the daily toolkit of everyworkingmathematician.In contrast,the formulationof the spectral theoremgiven below uses only the relativelyelementaryconcepts of measure theory.This formulationhas been part of the oral traditionof Hilbert space ...
Algebraic Proof Complexity: Progress, Frontiers and Challenges
... a polynomial-time function f from a set of finite strings over some given alphabet onto the set of propositional tautologies (reasonably encoded). Thus, f (x) = y means that the string x is a proof of the tautology y. Note that since f is onto, all tautologies and only tautologies have proofs (and t ...
... a polynomial-time function f from a set of finite strings over some given alphabet onto the set of propositional tautologies (reasonably encoded). Thus, f (x) = y means that the string x is a proof of the tautology y. Note that since f is onto, all tautologies and only tautologies have proofs (and t ...
Undergraduate algebra
... the rectangle have the same number of symmetries, but they are clearly symmetric in different ways. How can one capture this difference? Given two symmetries of some shape, we may transform the shape by the first one, and then apply the second one to the result. The operation obtained in this way is ...
... the rectangle have the same number of symmetries, but they are clearly symmetric in different ways. How can one capture this difference? Given two symmetries of some shape, we may transform the shape by the first one, and then apply the second one to the result. The operation obtained in this way is ...
![Elliptic curves with Q( E[3]) = Q( ζ3)](http://s1.studyres.com/store/data/012817289_1-48789e28be1e09d726c6f57e08e36eee-300x300.png)
