Terminalizations of quotients of Fano varieties of lines on cubic fourfolds

TL;DR

This paper classifies terminalizations of quotients of Fano varieties of lines on cubic fourfolds, computes topological invariants, and identifies new deformation classes of holomorphic symplectic varieties.

Contribution

It provides a classification of terminalizations for these quotients and introduces two new deformation classes of four-dimensional irreducible holomorphic symplectic varieties.

Findings

Computed second Betti number and fundamental group of the regular locus.

Identified two new deformation classes of symplectic varieties.

Classified projective terminalizations of the quotients.

Abstract

We classify projective terminalizations of quotients of Fano varieties of lines on smooth cubic fourfolds by finite groups of symplectic automorphisms of the underlying cubic. We compute the second Betti number and the fundamental group of the regular locus. As a consequence, we identify two new deformation classes of four-dimensional irreducible holomorphic symplectic varieties with second Betti number equal to four and simply connected regular locus.