Terminalizations of quotients of Fano varieties of lines on cubic fourfolds

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.