Prime order isometries of unimodular lattices and automorphisms of ihs manifolds

TL;DR

This paper classifies automorphisms of certain complex manifolds by analyzing isometries of unimodular lattices, providing a comprehensive understanding of their structure and symmetries.

Contribution

It introduces a complete classification of odd prime order non-symplectic automorphisms of irreducible holomorphic symplectic manifolds based on lattice isometry analysis.

Findings

Classified conjugacy classes of odd prime order isometries in unimodular lattices

Established a correspondence between lattice isometries and automorphisms of holomorphic symplectic manifolds

Provided a framework for understanding automorphism groups of these manifolds

Abstract

We characterize conjugacy classes of isometries of odd prime order in unimodular Z-lattices. This is applied to give a complete classification of odd prime order non-symplectic automorphisms of irreducible holomorphic symplectic manifolds up to deformation and birational conjugacy.