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作者：Buzzi, J
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Polytechnique de Paris; Ecole Polytechnique
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作者：Oh, YG; Park, JS
作者单位：University of Wisconsin System; University of Wisconsin Madison; Korea Institute for Advanced Study (KIAS)
摘要：In this paper, we study deformations of coisotropic submanifolds in a symplectic manifold. First we derive the equation that governs C-infinity deformations of coisotropic submanifolds and define the corresponding C-infinity-moduli space of coisotropic submanifolds modulo the Hamiltonian isotopies. This is a non-commutative and non-linear generalization of the well-known description of the local deformation space of Lagrangian submanifolds as the set of graphs of closed one forms in the Darbou...
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作者：Bergelson, V; Host, B; Kra, B; Ruzsa, I
作者单位：University System of Ohio; Ohio State University; Universite Gustave-Eiffel; Northwestern University; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Hungarian Academy of Sciences
摘要：Aiming at a simultaneous extension of Khintchine's and Furstenberg's Recurrence theorems, we address the question if for a measure preserving system (X, X, mu, T) and a set A is an element of X of positive measure, the set of integers n such that mu( A boolean AND T-n A boolean AND T-2n A boolean AND... boolean AND T-kn A) >mu( A)(k+1) - epsilon is syndetic. The size of this set, surprisingly enough, depends on the length (k + 1) of the arithmetic progression under consideration. In an ergodic...
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作者：Kable, AC; Yukie, A
作者单位：Oklahoma State University System; Oklahoma State University - Stillwater; Tohoku University
摘要：We show that the number of quintic number fields whose discriminant does not exceed X in absolute value is bounded by a constant times X1+epsilon for any epsilon > 0. This may be compared with the conjecture that the number of such fields is asymptotic to a constant times X as X tends to infinity.
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作者：Liebeck, MW; Shalev, A
作者单位：Imperial College London; Hebrew University of Jerusalem
摘要：Let Gamma be a Fuchsian group of genus at least 2 (at least 3 if Gamma is non-oriented). We study the spaces of homomorphisms from Gamma to finite simple groups G, and derive a number of applications concerning random generation and representation varieties. Precise asymptotic estimates for |Hom(Gamma, G)| are given, implying in particular that as the rank of G tends to infinity, this is of the form |G|(mu(Gamma)+ 1+ o(1)), where mu(Gamma) is the measure of G. We then prove that a randomly cho...
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作者：Favre, C; Jonsson, M
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; University of Michigan System; University of Michigan; Royal Institute of Technology
摘要：We show that valuations on the ring R of holomorphic germs in dimension 2 may be naturally evaluated on plurisubharmonic functions, giving rise to generalized Lelong numbers in the sense of Demailly. Any plurisubharmonic function thus defines a real-valued function on the set V of valuations on R and - by way of a natural Laplace operator defined in terms of the tree structure on V - a positive measure on V. This measure contains a great deal of information on the singularity at the origin. Un...
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作者：Chan, D; Ingalls, C
作者单位：University of New South Wales Sydney; University of New Brunswick
摘要：We develop the minimal model program for orders over surfaces and so establish a noncommutative generalisation of the existence and uniqueness of minimal algebraic surfaces. We define terminal orders and show that they have unique etale local structures. This shows that they are determined up to Morita equivalence by their centre and algebra of quotients. This reduces our problem to the study of pairs (Z,alpha) consisting of a surface Z and an element alpha of the Brauer group Brk(Z). We then ...
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作者：Junge, M
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：We use Voiculescu's concept of free probability to construct a completely isomorphic embedding of the operator space OH in the predual of a von Neumann algebra. We analyze the properties of this embedding and determine the operator space projection constant of OHn: 108(1) root 1 + ln(n) n (<=) P: B(l(2)) --> OHninf, P-2 = P parallel to P parallel to(cb) <= 288 pi root 1 + ln(2n) n. The lower estimate is a recent result of Pisier and Shlyakhtenko that improves an estimate of order 1/(1+ ln n) o...
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作者：Rollin, Y; Singer, M
作者单位：Massachusetts Institute of Technology (MIT)
摘要：A new construction is presented of scalar-flat Kahler metrics on non-minimal ruled surfaces. The method is based on the resolution of singularities of orbifold ruled surfaces which are closely related to rank-2 parabolically stable holomorphic bundles. This rather general construction is shown also to give new examples of low genus: in particular, it is shown that CP2 blown up at 10 suitably chosen points, admits a scalar-flat Kahler metric; this answers a question raised by Claude LeBrun in 1...
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作者：Caprace, PE; Mühlherr, B
作者单位：Universite Libre de Bruxelles
摘要：We give the solution of the isomorphism problem for Kac-Moody groups over algebraically closed fields of any characteristic. In particular, we prove a conjecture of Kac and Peterson and compute the automorphism group of a Kac-Moody group over an algebraically closed field of characteristic zero.
