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https://hdl.handle.net/2445/194431
Title: | Stability conditions in families |
Author: | Lahoz Vilalta, Martí Bayer, Arend Macrì, Emanuel Nuer, Howard Perry, Alexander Stellari, Paolo |
Keywords: | Geometria algebraica Homologia Categories (Matemàtica) Varietats simplèctiques Algebraic geometry Homology Categories (Mathematics) Symplectic manifolds |
Issue Date: | 17-May-2021 |
Publisher: | Springer |
Abstract: | We develop a theory of Bridgeland stability conditions and moduli spaces of semistable objects for a family of varieties. Our approach is based on and generalizes previous work by Abramovich-Polishchuk, Kuznetsov, Lieblich, and Piyaratne-Toda. Our notion includes openness of stability, semistable reduction, a support property uniformly across the family, and boundedness of semistable objects. We show that such a structure exists whenever stability conditions are known to exist on the fibers. Our main application is the generalization of Mukai's theory for moduli spaces of semistable sheaves on K3 surfaces to moduli spaces of Bridgeland semistable objects in the Kuznetsov component associated to a cubic fourfold. This leads to the extension of theorems by Addington-Thomas and Huybrechts on the derived category of special cubic fourfolds, to a new proof of the integral Hodge conjecture, and to the construction of an infinite series of unirational locally complete families of polarized hyperkähler manifolds of K3 type. Other applications include the deformation-invariance of Donaldson-Thomas invariants counting Bridgeland stable objects on Calabi-Yau threefolds, and a method for constructing stability conditions on threefolds via degeneration. |
Note: | Reproducció del document publicat a: https://doi.org/10.1007/s10240-021-00124-6 |
It is part of: | Publications mathématiques de l'IHÉS, 2021, num. 133, p. 157-325 |
URI: | https://hdl.handle.net/2445/194431 |
Related resource: | https://doi.org/10.1007/s10240-021-00124-6 |
ISSN: | 0073-8301 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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