Algebraically trivial automorphisms of irreducible holomorphic symplectic manifolds

TL;DR

This paper classifies algebraically trivial automorphisms of irreducible holomorphic symplectic manifolds using lattice theory, focusing on automorphisms of even order and their existence across different deformation types.

Contribution

It extends existing lattice-theoretic methods to classify algebraically trivial automorphisms, including non-symplectic cases, up to deformation and birational conjugacy.

Findings

Classifies even order algebraically trivial nonsymplectic automorphisms

Shows existence of certain automorphisms only for finitely many deformation types

Extends lattice-theoretic approach to broader class of automorphisms

Abstract

We extend the lattice-theoretic approach of Brandhorst--Cattaneo to classify algebraically trivial actions on the known IHS manifolds, up to deformation and birational conjugacy. In particular, we classify even order algebraically trivial nonsymplectic automorphisms, with or without trivial discriminant action. In the case of nontrivial discriminant actions, we show that such automorphisms exist only for finitely many known deformation types and orders.