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作者：Diverio, Simone; Merker, Joel; Rousseau, Erwan
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Sapienza University Rome; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
摘要：We show that for every smooth projective hypersurface X subset of Pn+1 of degree d and of arbitrary dimension n >= 2, if X is generic, then there exists a proper algebraic subvariety Y not subset of X such that every nonconstant entire holomorphic curve f : C -> X has image f (C) which lies in Y, as soon as its degree satisfies the effective lower bound d >= 2(n5).
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作者：Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T.
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Toronto; Massachusetts Institute of Technology (MIT); Kobe University; University of California System; University of California Los Angeles
摘要：We consider the cubic defocusing nonlinear Schrodinger equation on the two dimensional torus. We exhibit smooth solutions for which the support of the conserved energy moves to higher Fourier modes. This behavior is quantified by the growth of higher Sobolev norms: given any delta << 1, K >> 1, s > 1, we construct smooth initial data u(0) with parallel to u(0)parallel to(s)(H) < delta, so that the corresponding time evolution u satisfies parallel to u(T)parallel to(Hs) > K at some time T. This...
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作者：Buchweitz, Ragnar-Olaf; Leuschke, Graham J.; Van den Bergh, Michel
作者单位：Syracuse University; University of Toronto; University Toronto Scarborough; Hasselt University
摘要：We show that determinantal varieties defined by maximal minors of a generic matrix have a non-commutative desingularization, in that we construct a maximal Cohen-Macaulay module over such a variety whose endomorphism ring is Cohen-Macaulay and has finite global dimension. In the case of the determinant of a square matrix, this gives a non-commutative crepant resolution.
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作者：Hausel, Tamas
作者单位：University of Oxford
摘要：We prove a generating function formula for the Betti numbers of Nakajima quiver varieties. We prove that it is a q-deformation of the Weyl-Kac character formula. In particular this implies that the constant term of the polynomial counting the number of absolutely indecomposable representations of a quiver equals the multiplicity of a certain weight in the corresponding Kac-Moody algebra, which was conjectured by Kac in 1982.
