On natural deformations of symplectic automorphisms of manifolds of K3^[n] type

TL;DR

This paper characterizes when finite symplectic automorphism groups of K3^[n] type manifolds can be deformed from natural automorphisms of K3 surfaces, based on a specific numerical criterion.

Contribution

It establishes a precise numerical condition that determines when such automorphisms are deformable from K3 surfaces.

Findings

Finite symplectic automorphism groups can be obtained via deformation under a numerical condition.

The paper provides a criterion to identify deformable automorphisms.

Deformation theory links automorphisms of K3 surfaces to higher-dimensional manifolds.

Abstract

In the present paper we prove that finite symplectic groups of automorphisms of manifolds of k3^[n] type can be obtained by deforming natural morphisms arising from K3 surfaces if and only if they satisfy a certain numerical condition.