Symplectic rigidity of O'Grady's tenfolds

TL;DR

This paper proves that all finite order symplectic automorphisms of O'Grady's 10-dimensional irreducible holomorphic symplectic manifolds are trivial, establishing a rigidity property for these complex structures.

Contribution

It demonstrates the symplectic rigidity of O'Grady's tenfolds by showing all finite order automorphisms are trivial, a new result in the study of these manifolds.

Findings

Finite order symplectic automorphisms are trivial

Supports the rigidity conjecture for O'Grady's tenfolds

Advances understanding of automorphism groups in hyperkähler geometry

Abstract

We prove that any symplectic automorphism of finite order of an irreducible holomorphic symplectic manifold of O'Grady's 10-dimensional deformation type is trivial.