EPW-sextics: taxonomy

TL;DR

This paper classifies EPW-sextics, special degree 6 hypersurfaces with hyperkähler double covers, focusing on those with positive-dimensional singular loci, and explores their moduli and period relations.

Contribution

It provides a classification of EPW-sextics with positive-dimensional singular loci, advancing understanding of their moduli space and period structures.

Findings

Classification of EPW-sextics with positive-dimensional singular loci

Analysis of their moduli space

Insights into period relations of double EPW-sextics

Abstract

An EPW-sextic is a special 4-dimensional hypersurfaces of degree 6 which comes equipped with a double cover which generically is a Hyperkaehler 4-fold deformation equivalent to the Hilbert square of a K3 surface. The family of EPW-sextics is analogous to the family of cubic 4-fold hypersurfaces, more precisely double EPW-sextics are analogous to varieties of lines on cubic 4-folds. This first paper in a series on moduli and periods of double EPW-sextics is mainly concerned with the classification of EPW-sextics which are analogous to cubic 4-folds whose singular locus has strictly positive dimension.