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作者：Bayer, Arend; Macri, Emanuele
作者单位：University of Edinburgh; University System of Ohio; Ohio State University
摘要：We use wall-crossing with respect to Bridgeland stability conditions to systematically study the birational geometry of a moduli space of stable sheaves on a K3 surface : (a) We describe the nef cone, the movable cone, and the effective cone of in terms of the Mukai lattice of . (b) We establish a long-standing conjecture that predicts the existence of a birational Lagrangian fibration on whenever admits an integral divisor class of square zero (with respect to the Beauville-Bogomolov form). T...
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作者：Iyama, Osamu; Wemyss, Michael
作者单位：Nagoya University; University of Edinburgh; Heriot Watt University
摘要：We first generalize classical Auslander-Reiten duality for isolated singularities to cover singularities with a one-dimensional singular locus. We then define the notion of CT modules for non-isolated singularities and we show that these are intimately related to noncommutative crepant resolutions (NCCRs). When R has isolated singularities, CT modules recover the classical notion of cluster tilting modules but in general the two concepts differ. Then, wanting to generalize the notion of NCCRs ...
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作者：Baranski, Krzysztof; Fagella, Nuria; Jarque, Xavier; Karpinska, Boguslawa
作者单位：University of Warsaw; University of Barcelona; Warsaw University of Technology
摘要：We prove that every transcendental meromorphic map f with disconnected Julia set has a weakly repelling fixed point. This implies that the Julia set of Newton's method for finding zeroes of an entire map is connected. Moreover, extending a result of Cowen for holomorphic self-maps of the disc, we show the existence of absorbing domains for holomorphic self-maps of hyperbolic regions, whose iterates tend to a boundary point. In particular, the results imply that periodic Baker domains of Newton...
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作者：Benson, David J.; Grodal, Jesper; Henke, Ellen
作者单位：University of Aberdeen; University of Copenhagen
摘要：We show that if an inclusion of finite groups Ha parts per thousand currency signG of index prime to p induces a homeomorphism of mod p cohomology varieties, or equivalently an F-isomorphism in mod p cohomology, then H controls p-fusion in G, if p is odd. This generalizes classical results of Quillen who proved this when H is a Sylow p-subgroup, and furthermore implies a hitherto difficult result of Mislin about cohomology isomorphisms. For p=2 we give analogous results, at the cost of replaci...
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作者：Bourgain, Jean; Kontorovich, Alex
作者单位：Institute for Advanced Study - USA; Yale University
摘要：We prove that a set of density one satisfies the local-global conjecture for integral Apollonian gaskets. That is, for a fixed integral, primitive Apollonian gasket, almost every (in the sense of density) admissible (passing local obstructions) integer is the curvature of some circle in the gasket.
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作者：Deligne, Pierre
作者单位：Institute for Advanced Study - USA
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作者：Bhatt, Bhargav; Blickle, Manuel; Lyubeznik, Gennady; Singh, Anurag K.; Zhang, Wenliang
作者单位：Institute for Advanced Study - USA; Johannes Gutenberg University of Mainz; University of Minnesota System; University of Minnesota Twin Cities; Utah System of Higher Education; University of Utah; University of Nebraska System; University of Nebraska Lincoln
摘要：Let R be a commutative Noetherian ring that is a smooth -algebra. For each ideal of R and integer k, we prove that the local cohomology module has finitely many associated prime ideals. This settles a crucial outstanding case of a conjecture of Lyubeznik asserting this finiteness for local cohomology modules of all regular rings.
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作者：Brendle, Simon; Eichmair, Michael
作者单位：Stanford University; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We give examples of asymptotically flat three-manifolds which admit arbitrarily large constant mean curvature spheres that are far away from the center of the manifold. This resolves a question raised by Huisken and Yau (Invent Math 124:281-311, 1996). On the other hand, we show that such surfaces cannot exist when has nonnegative scalar curvature. This result depends on an intricate relationship between the scalar curvature of the initial data set and the isoperimetric ratio of large stable c...
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作者：Kodama, Yuji; Williams, Lauren
作者单位：University System of Ohio; Ohio State University; University of California System; University of California Berkeley
摘要：Soliton solutions of the KP equation have been studied since 1970, when Kadomtsev and Petviashvili proposed a two-dimensional nonlinear dispersive wave equation now known as the KP equation. It is well-known that one can use the Wronskian method to construct a soliton solution to the KP equation from each point of the real Grassmannian Gr(k,n). More recently, several authors (Biondini and Chakravarty, J Math Phys 47:033514, 2006; Biondini and Kodama, J. Phys A Math Gen 36:10519-10536, 2003; Ch...
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作者：Colding, Tobias Holck; Minicozzi, William P., II
作者单位：Massachusetts Institute of Technology (MIT); Johns Hopkins University
摘要：We show that for any Ricci-flat manifold with Euclidean volume growth the tangent cone at infinity is unique if one tangent cone has a smooth cross-section. Similarly, for any noncollapsing limit of Einstein manifolds with uniformly bounded Einstein constants, we show that local tangent cones are unique if one tangent cone has a smooth cross-section.
