Non-symplectic automorphisms of prime order of O'Grady's tenfolds and cubic fourfolds

TL;DR

This paper classifies non-symplectic automorphisms of prime order on OG10 type hyperkähler manifolds using lattice theory, relates them to automorphisms of cubic fourfolds, and discusses implications for the rationality of certain fourfolds.

Contribution

It provides a lattice-theoretic classification of these automorphisms and links them to automorphisms of cubic fourfolds, advancing understanding of their geometric and algebraic structures.

Findings

Classified non-symplectic automorphisms of prime order on OG10 manifolds.

Connected automorphisms of cubic fourfolds to those on associated LSV manifolds.

Discussed implications for the rationality conjecture of cubic fourfolds.

Abstract

We give a lattice-theoretic classification of non-symplectic automorphisms of prime order of irreducible holomorphic symplectic manifolds of OG10 type. We determine which automorphisms are induced by a non-symplectic automorphism of prime order of a cubic fourfold on the associated LSV manifolds, giving a geometric and lattice-theoretic description of the algebraic and transcendental lattices of the cubic fourfold. As an application we discuss the rationality conjecture for a general cubic fourfold with a non-symplectic automorphism of prime order.