• Corpus ID: 209376165

Stability conditions and moduli spaces for Kuznetsov components of Gushel-Mukai varieties

@article{Perry2019StabilityCA,
  title={Stability conditions and moduli spaces for Kuznetsov components of Gushel-Mukai varieties},
  author={Alexander Perry and Laura Pertusi and Xiaolei Zhao},
  journal={arXiv: Algebraic Geometry},
  year={2019}
}
We prove the existence of Bridgeland stability conditions on the Kuznetsov components of Gushel-Mukai varieties, and describe the structure of moduli spaces of Bridgeland semistable objects in these categories in the even-dimensional case. As applications, we construct a new infinite series of unirational locally complete families of polarized hyperkahler varieties of K3 type, and characterize Hodge-theoretically when the Kuznetsov component of an even-dimensional Gushel-Mukai variety is… 
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20 Citations
Highly Influential Citations
1
Background Citations
7
Methods Citations
3

20 Citations

Stability conditions on Kuznetsov components of Gushel-Mukai threefolds and Serre functor
We show that the stability conditions on the Kuznetsov component of a Gushel–Mukai threefold, constructed by Bayer, Lahoz, Macrì and Stellari, are preserved by the Serre functor, up to the action of…
BRIDGELAND MODULI SPACES AND KUZNETSOV’S FANO THREEFOLD CONJECTURE
We study the Hilbert scheme H of twisted cubics on a special smooth Gushel-Mukai threefolds X10. We show that it is a smooth irreducible projective threefold if X10 is general among special…
Some Motivic Properties of Gushel-Mukai Sixfolds
Gushel-Mukai sixfolds are an important class of so-called FanoK3 varieties. In this paper we show that they admit a multiplicative ChowKünneth decomposition modulo algebraic equivalence and that they…
Marked and Labelled Gushel–Mukai Fourfolds
We prove that the moduli stacks of marked and labelled Hodge-special Gushel-Mukai fourfolds are isomorphic. As an application, we construct rational maps from the stack of Hodge-special Gushel-Mukai…
Stability conditions in families
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…
The integral Hodge conjecture for two-dimensional Calabi–Yau categories
We formulate a version of the integral Hodge conjecture for categories, prove the conjecture for two-dimensional Calabi–Yau categories which are suitably deformation equivalent to the derived…
A moduli theoretic approach to Lagrangian subvarieties of hyperk\"ahler varieties: Examples
. We propose two conjectures on a moduli theoretic approach to constructing Lagrangian subvarieties of hyperk¨ahler varieties arising from the Kuznetsov components of cubic fourfolds or Gushel–Mukai…
Derived categories of hearts on Kuznetsov components
We prove a general criterion which guarantees that an admissible subcategory K of the derived category of an abelian category is equivalent to the bounded derived category of the heart of a bounded…
Conics on Gushel-Mukai fourfolds, EPW sextics and Bridgeland moduli spaces
We identify the double dual EPW sextic ỸA⊥ and the double EPW sextic ỸA, associated with a very general Gushel-Mukai fourfold X , with the Bridgeland moduli spaces of stable objects of character Λ1…
Serre functors and dimensions of residual categories
We describe in terms of spherical twists the Serre functors of many interesting semiorthogonal components, called residual categories, of the derived categories of projective varieties. In…
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