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作者：Massot, Patrick; Niederkrueger, Klaus; Wendl, Chris
作者单位：Universite Paris Saclay; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; University of London; University College London
摘要：For contact manifolds in dimension three, the notions of weak and strong symplectic fillability and tightness are all known to be inequivalent. We extend these facts to higher dimensions: in particular, we define a natural generalization of weak fillings and prove that it is indeed weaker (at least in dimension five), while also being obstructed by all known manifestations of overtwistedness. We also find the first examples of contact manifolds in all dimensions that are not symplectically fil...
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作者：Ovrelid, Nils; Vassiliadou, Sophia
作者单位：University of Oslo; Georgetown University
摘要：Let X be a pure n-dimensional (where na parts per thousand yen2) complex analytic subset in a, (N) with an isolated singularity at 0. In this paper we express the L (2)-(0,q)--cohomology groups for all q with 1a parts per thousand currency signqa parts per thousand currency signn of a sufficiently small deleted neighborhood of the singular point in terms of resolution data. We also obtain identifications of the L (2)-(0,q)--cohomology groups of the smooth points of X, in terms of resolution da...
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作者：Molev, A. I.
作者单位：University of Sydney
摘要：For each simple Lie algebra consider the corresponding affine vertex algebra at the critical level. The center of this vertex algebra is a commutative associative algebra whose structure was described by a remarkable theorem of Feigin and Frenkel about two decades ago. However, only recently simple formulas for the generators of the center were found for the Lie algebras of type A following Talalaev's discovery of explicit higher Gaudin Hamiltonians. We give explicit formulas for generators of...
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作者：Hacon, Christopher D.; Xu, Chenyang
作者单位：Utah System of Higher Education; University of Utah
摘要：Let f:X -> U be a projective morphism of normal varieties and (X,Delta) a dlt pair. We prove that if there is an open set U (0)aS,U, such that (X,Delta)x (U) U (0) has a good minimal model over U (0) and the images of all the non-klt centers intersect U (0), then (X,Delta) has a good minimal model over U. As consequences we show the existence of log canonical compactifications for open log canonical pairs, and the fact that the moduli functor of stable schemes satisfies the valuative criterion...
