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Bayer Arend Lahoz Martí Macrì Emanuele Nuer Howard Perry Alexander Stellari Paolo 《Publications Mathématiques de L'IHéS》2021,133(1):157-325
Publications mathématiques de l'IHÉS - We develop a theory of Bridgeland stability conditions and moduli spaces of semistable objects for a family of varieties. Our approach is based... 相似文献
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Marcello Bernardara Emanuele Macrì Sukhendu Mehrotra Paolo Stellari 《Advances in Mathematics》2012,229(2):770-803
We prove a categorical version of the Torelli theorem for cubic threefolds. More precisely, we show that the non-trivial part of a semi-orthogonal decomposition of the derived category of a cubic threefold characterizes its isomorphism class. 相似文献
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We prove that the Fano variety of lines of a generic cubic fourfold containing a plane is isomorphic to a moduli space of twisted stable complexes on a K3 surface. On the other hand, we show that the Fano varieties are always birational to moduli spaces of twisted stable coherent sheaves on a K3 surface. The moduli spaces of complexes and of sheaves are related by wall-crossing in the derived category of twisted sheaves on the corresponding K3 surface. 相似文献
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We prove that the kernels of Fourier–Mukai functors are not unique in general. On the other hand we show that the cohomology sheaves of those kernels are unique. We also discuss several properties of the functor sending an object in the derived category of the product of two smooth projective schemes to the corresponding Fourier–Mukai functor. 相似文献
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Paolo Stellari 《Geometriae Dedicata》2004,108(1):1-14
In this paper we describe some results about K3 surfaces with Picard number 1 and 2. In particular, we give a new simple proof of a theorem due to Oguiso which shows that,
given an integer N, there is a K3 surface with Picard number 2 and at least N non-isomorphic FM-partners. We describe also the Mukai vectors of the moduli spaces associated to the FM-partners of K3 surfaces with Picard number 1. 相似文献
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We provide a simple proof of the existence of internal Homs in the localization of the category of dg categories with respect to all quasi-equivalences and of some of their main properties such as the so-called derived Morita theory. This was originally proved in a seminal paper by Toën. 相似文献
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Paolo Stellari 《Transactions of the American Mathematical Society》2008,360(12):6631-6642
We consider the natural action of a finite group on the moduli space of polarized K3 surfaces which induces a duality defined by Mukai for surfaces of this type. We show that the group permutes polarized Fourier-Mukai partners of polarized K3 surfaces and we study the divisors in the fixed loci of the elements of this finite group.
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Paolo Stellari 《Mathematische Zeitschrift》2007,256(2):425-441
We prove that if two abelian varieties have equivalent derived categories then the derived categories of the smooth stacks
associated to the corresponding Kummer varieties are equivalent as well. The second main result establishes necessary and
sufficient conditions for the existence of equivalences between the twisted derived categories of two Kummer surfaces in terms
of Hodge isometries between the generalized transcendental lattices of the corresponding abelian surfaces.
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We prove that two derived equivalent twisted K3 surfaces have isomorphic periods. The converse is shown for K3 surfaces with large Picard number. It is also shown that all possible twisted derived equivalences between arbitrary twisted K3 surfaces form a subgroup of the group of all orthogonal transformations of the cohomology of a K3 surface.The passage from twisted derived equivalences to an action on the cohomology is made possible by twisted Chern characters that will be introduced for arbitrary smooth projective varieties. 相似文献
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