• 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… 
View PDF on arXiv
19 Citations
Highly Influential Citations
1
Background Citations
5
Methods Citations
3

19 Citations

Citation Type

Citation Type

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…
...
...

References

SHOWING 1-10 OF 49 REFERENCES
Gushel–Mukai varieties: Moduli
We describe the moduli stack of Gushel–Mukai varieties as a global quotient stack and its coarse moduli space as the corresponding GIT quotient. The construction is based on a comprehensive study of…
Derived categories of Gushel–Mukai varieties
We study the derived categories of coherent sheaves on Gushel–Mukai varieties. In the derived category of such a variety, we isolate a special semiorthogonal component, which is a K3 or Enriques…
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…
Gushel–Mukai varieties: Linear spaces and periods
Beauville and Donagi proved in 1985 that the primitive middle cohomology of a smooth complex cubic fourfold and the primitive second cohomology of its variety of lines, a smooth hyperk\"ahler…
Stability conditions on Kuznetsov components
We introduce a general method to induce Bridgeland stability conditions on semiorthogonal decompositions. In particular, we prove the existence of Bridgeland stability conditions on the Kuznetsov…
Semistable sheaves in positive characteristic
We prove Maruyama’s conjecture on the boundedness of slope semistable sheaves on a projective variety defined over a noetherian ring. Our approach also gives a new proof of the boundedness for…
Projectivity and birational geometry of Bridgeland moduli spaces
We construct a family of nef divisor classes on every moduli space of stable complexes in the sense of Bridgeland. This divisor class varies naturally with the Bridgeland stability condition. For a…
On the double EPW sextic associated to a Gushel–Mukai fourfold
TLDR
It is proved that $\tilde{Y}_A$ is birational to the Hilbert scheme of points of length two on a K3 surface if and only if the Gushel-Mukai fourfold is Hodge-special with discriminant $d$ such that the negative Pell equation $\mathcal{P}_{d/2}(-1)$ is solvable in $\mathbb{Z}$.
Gushel--Mukai varieties: classification and birationalities
We perform a systematic study of Gushel-Mukai varieties---quadratic sections of linear sections of cones over the Grassmannian Gr(2,5). This class of varieties includes Clifford general curves of…
Symplectic structures on moduli spaces of sheaves via the Atiyah class
...
...