The geometry of antisymplectic involutions, I

Abstract

We study fixed loci of antisymplectic involutions on projective hyperkähler manifolds. When the involution is induced by an ample class of square 2 in the Beauville-Bogomolov-Fujiki lattice, we show that the number of connected components of the fixed locus is equal to the divisibility of the class, which is either 1 or 2.

Equivariant geometry of odd-dimensional complete intersections of two quadrics

“…We elaborate on constructions of Reid [Rei72], Desale-Ramanan [DR77], Donagi [Don80], and Bhargava-Gross-Wang [BGW17,Wan18] from a functorial/moduli perspective applicable to equivariant analysis. We also present a new connection with hyperkähler geometry (see Section 5), extending Kummer-type constructions to higher dimensions; connections between Fano and hyperkähler geometry are in the focus of many recent studies, including [FMOS21].…”