## Evento

Quando: 06/06/2018 - 14:45

Dove: Palazzo Campana - TORINO

Aula: Aula C

Relatore: Emanuele Macrì

Afferenza: Northeastern University

Locandina:

## Descrizione:

The aim of the talk is to study smooth projective hyperkähler fourfolds

which are deformations of Hilbert squares of K3 surfaces and are equipped

with a polarization of fixed degree and divisibility. These are

parametrized by a quasi-projective irreducible 20-dimensional moduli space

and Verbitksy’s Torelli theorem implies that their period map is an open

embedding.

Our main result is that the complement of the image of the period map is a

finite union of explicit Heegner divisors that we describe. We will also

comment on the higher dimensional case.

The key technical ingredient is the description of the nef and movable cone

for projective hyperkähler manifolds (deformation equivalent of Hilbert

schemes of K3 surfaces) by Bayer, Hassett, and Tschinkel. As an application

we will present a new short proof (by Bayer and Mongardi) for the

celebrated result by Laza and Looijenga on the image of the period map for

cubic fourfolds. If time permits, as second application, we will show that

infinitely many Heegner divisors in a given period space have the property

that their general points correspond to fourfolds which are isomorphic to

Hilbert squares of a K3 surfaces, or to double EPW sextics.

This is joint work with Olivier Debarre.