# Divisors in the moduli space of Debarre-Voisin varieties

@inproceedings{Benedetti2021DivisorsIT, title={Divisors in the moduli space of Debarre-Voisin varieties}, author={Vladimiro Benedetti and Jieao Song}, year={2021} }

Let V10 be a 10-dimensional complex vector space and let σ ∈ ∧ V ∨ 10 be a non-zero alternating 3-form. One can define several associated degeneracy loci: the Debarre– Voisin variety X 6 ⊂ Gr(6, V10), the Peskine variety X 1 ⊂ P(V10), and the hyperplane section X 3 ⊂ Gr(3, V10). Their interest stems from the fact that the Debarre–Voisin varieties form a locally complete family of projective hyperkähler fourfolds of K3-type. We prove that when smooth, the varieties X 6 , X 1 , and X 3 share one…

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## References

SHOWING 1-10 OF 44 REFERENCES

Modular sheaves on hyperkähler varieties

- MathematicsAlgebraic Geometry
- 2022

A torsion free sheaf on a hyperkahler variety $X$ is modular if the discriminant satisfies a certain condition, for example if it is a multiple of $c_2(X)$ the sheaf is modular. The definition is…

On the period map for polarized hyperk\"ahler fourfolds

- Mathematics
- 2017

This is an improved version of the eprint previously entitled "Unexpected isomorphisms between hyperkahler fourfolds."
We study smooth projective hyperkahler fourfolds that are deformations of…

Fano varieties of cubic fourfolds containing a plane

- Mathematics
- 2009

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…

Pfaffian bundles on cubic surfaces and configurations of planes

- Mathematics
- 2012

We construct a canonical birational map between the moduli space of Pfaffian vector bundles on a cubic surface and the space of complete pentahedra inscribed in the cubic surface. The universal…

Hilbert squares of K3 surfaces and Debarre-Voisin varieties

- MathematicsJournal de l’École polytechnique — Mathématiques
- 2020

The Debarre-Voisin hyperk\"ahler fourfolds are built from alternating $3$-forms on a $10$-dimensional complex vector space, which we call trivectors. They are analogous to the Beauville-Donagi…

Nested varieties of K3 type

- Mathematics
- 2019

Using geometrical correspondences induced by projections and two-steps flag varieties, and a generalization of Orlov's projective bundle theorem, we relate the Hodge structures and derived categories…

Special Cubic Fourfolds

- MathematicsCompositio Mathematica
- 2000

AbstractA cubic fourfold is a smooth cubic hypersurface of dimension four; it is special if it contains a surface not homologous to a complete intersection. Special cubic fourfolds form a countably…

A survey of Torelli and monodromy results for holomorphic-symplectic varieties

- Mathematics
- 2011

We survey recent results about the Torelli question for holomorphicsymplectic varieties. Following are the main topics. A Hodge theoretic Torelli theorem. A study of the subgroup WExc, of the…

Orbital degeneracy loci and applications.

- Mathematics
- 2017

Degeneracy loci of morphisms between vector bundles have been used in a wide variety of situations. We introduce a vast generalization of this notion, based on orbit closures of algebraic groups in…

Geometry of orbit closures for the representations associated to gradings of Lie algebras of types $E_7$

- Mathematics
- 2013

This paper is a continuation of (KW11a). We investigate the orbit clo- sures for the class of representations of simple algebraic groups associated to various gradings on the simple Lie algebra of…