Related papers: EPW-sextics: taxonomy

EPW-sextics are special 4-dimensional sextic hypersurfaces (with 20 moduli) which come equipped with a double cover. We analyze the double cover of EPW-sextics parametrized by a certain prime divisor in the moduli space. We associate to the…

Eisenbud Popescu and Walter have constructed certain special 4-dimensional sextic hypersurfaces as Lagrangian degeneracy loci. We prove that the natural double cover of a generic EPW-sextic is a deformation of the Hilbert square of a…

A locally complete family of projective symplectic 4-folds is provided by natural double covers of Eisenbud-Popescu-Walter (EPW) sextic hypersurfaces in projective 5-space. The dual of an EPW sextic is another EPW sextic, thus to a double…

We construct a new 20-dimensional family of projective 6-dimensional irreducible holomorphic symplectic manifolds. The elements of this family are deformation equivalent with the Hilbert scheme of three points on a K3 surface and are…

We study a correspondence between double EPW cubes and double EPW sextics, two families of polarized hyper-K\"ahler manifolds related to Gushel--Mukai fourfolds. We infer relations between these families in terms of Hodge structures and…

Works by O'Grady allow to associate to a 2-dimensional Gushel-Mukai variety, which is a K3 surface, a double EPW sextic. We characterize the K3 surfaces whose associated double EPW sextic is smooth. As a consequence, we are able to produce…

O'Grady showed that certain special sextics in $\mathbb{P}^5$ called EPW sextics admit smooth double covers with a holomorphic symplectic structure. We propose another perspective on these symplectic manifolds, by showing that they can be…

Double EPW quartics are hyperk\"ahler varieties of dimension 4, first introduced by Iliev, Kapustka, Kapustka, and Ranestad. The general double EPW quartic is isomorphic to a moduli space of twisted sheaves on a $K3$ surface. They have a…

EPW cubes form a locally complete family of smooth projective hyper-K\"ahler varieties of dimension 6, constructed by Iliev--Kapustka--Kapustka--Ranestad.\ Their construction and behavior share a lot of similarities with the double EPW…

In analogy to the case of cubic fourfolds, we discuss the conditions under which the double cover $\tilde{Y}_A$ of the EPW sextic hypersurface associated to a Gushel-Mukai fourfold is birationally equivalent to a moduli space of (twisted)…

We show that the double dual EPW sextic associated with a strongly smooth Gushel-Mukai surface can be realized as a moduli space of semistable objects on its bounded derived category. Also, we observe that the double dual EPW surface…

We construct two examples of projective hyper-K\"ahler fourfolds of K3[2]-type with an action of the alternating group A7, making them some of the most symmetric hyper-K\"ahler fourfolds. They are realized as so called double EPW sextics…

We study the indeterminacy locus of the period map for double EPW-sextics. We recall that double EPW-sextics are parametrized by lagrangian subspaces of the third wedge-product of a 6-dimensional complex vector-space. The indeterminacy…

A generic K3 surface of degree 2t is a general complex projective K3 surface whose Picard group is generated by the class of an ample divisor whose with respect to the intersection form is 2t. We show that if X is the Hilbert square of a…

The Chow rings of hyperK\"ahler varieties are conjectured to have a particularly rich structure. In this paper, we focus on the locally complete family of double EPW sextics and establish some properties of their Chow rings. First we prove…

The Eckardt hypersurface in $\mathbb{P}^{19}$ parameterizes smooth cubic surfaces with an Eckardt point, which is a point common to three of the $27$ lines on a smooth cubic surface. We describe the cubic surfaces lying on the singular…

First steps towards a classification of irreducible symplectic 4-folds whose integral 2-cohomology with 4-tuple cup product is isomorphic to that of Hilb^2(K3). We prove that any such 4-fold deforms to an irreducible symplectic 4-fold of…

We study the geometry of a Picard modular fourfold which parametrizes abelian fourfolds of Weil type for the field of cube roots of unity. We find a projective model of this fourfold as a singular, degree ten, hypersurface X in projective…

Motivated by the Beauville-Voisin conjecture about Chow rings of powers of $K3$ surfaces, we consider a similar conjecture for Chow rings of powers of EPW sextics. We prove part of this conjecture for the very special EPW sextic studied by…

We explain a general construction of double covers of quadratic degeneracy loci and Lagrangian intersection loci based on reflexive sheaves. We relate the double covers of quadratic degeneracy loci to the Stein factorizations of the…