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作者：Schiffmann, Olivier
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作者：Benoist, Y
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS)
摘要：Let Omega be an indecomposable properly convex open subset of the real projective 3-space which is divisible i.e. for which there exists a torsion free discrete group Gamma of projective transformations preserving Omega such that the quotient M := Gamma\Omega is compact. We study the structure of M and of partial derivative Omega, when Omega is not strictly convex: The union of the properly embedded triangles in Omega projects in M onto an union of finitely many disjoint tori and Klein bottles...
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作者：Gan, SB; Wen, L
作者单位：Peking University
摘要：We give an affirmative answer to a problem of Liao and Mane which asks whether, for a nonsingular flow to loose the Omega-stability, it must go through a critical-element-bifurcation. More precisely, a vector field S on a compact boundaryless manifold is called a star system if S has a C-1 neighborhood U in the set of C-1 vector fields such that every singularity and every periodic orbit of every X epsilon U is hyperbolic. We prove that any nonsingular star flow satisfies Axiom A and the no cy...
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作者：Alon, N; Makarychev, K; Makarychev, Y; Naor, A
作者单位：Tel Aviv University; Tel Aviv University; Institute for Advanced Study - USA; Princeton University; Microsoft
摘要：We introduce a new graph parameter, called the Grothendieck constant of a graph G = ( V, E), which is defined as the least constant K such that for every A : E --> R, sup(f:V -->S\V\-1{u, v} is an element of E) Sigma A(u, v) . [f(u), f(v)] <= K sup(phi:V --> {-1, +1} {u, v} is an element of E) Sigma A(u, v) . phi*u)phi(v). The classical Grothendieck inequality corresponds to the case of bipartite graphs, but the case of general graphs is shown to have various algorithmic applications. Indeed, ...
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作者：Rosenschon, Andreas; Ostvaer, Paul Arne
作者单位：State University of New York (SUNY) System; University at Buffalo, SUNY; University of Alberta; University of Oslo
摘要：Assume F is a homotopy invariant pseudo pretheory with torsion values and X is a smooth scheme of finite type over a field k. We show for certain field extensions k subset of K the map F(X) --> F(X-K ) is an isomorphism.
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作者：Vakil, R
作者单位：Stanford University
摘要：We consider the question: How bad can the deformation space of an object be? The answer seems to be: Unless there is some a priori reason otherwise, the deformation space may be as bad as possible. We show this for a number of important moduli spaces. More precisely, every singularity of finite type over Zeta (up to smooth parameters) appears on: the Hilbert scheme of curves in projective space; and the moduli spaces of smooth projective general-type surfaces (or higher-dimensional varieties),...
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作者：Constantin, Adrian
作者单位：Trinity College Dublin; Lund University
摘要：Analyzing a free boundary problem for harmonic functions we show that there are no closed particle paths in an irrotational inviscid traveling wave propagating at the surface of water over a flat bed: within a period each particle experiences a backward-forward motion with a slight forward drift.
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作者：McMullen, Curtis T.
作者单位：Harvard University
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作者：Labourie, Francois
作者单位：Universite Paris Saclay
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作者：Hassett, B; Tschinkel, Y
作者单位：Rice University
摘要：We prove that rationally connected varieties over the function field of a complex curve satisfy weak approximation for places of good reduction.
