On symplectic automorphisms of hyperk\"ahler fourfolds of K3^[2] type

TL;DR

This paper classifies symplectic automorphisms of certain hyperk"ahler fourfolds, showing they are contained in the group Co_1, and provides an example of an order 11 automorphism on a Fano scheme.

Contribution

It proves that finite symplectic automorphism groups of hyperk"ahler fourfolds of K3^[2] type are contained in the group Co_1 and constructs a specific automorphism of order 11.

Findings

Symplectic automorphism groups are contained in Co_1

Constructed an order 11 symplectic automorphism example

Enhanced understanding of automorphisms of hyperk"ahler fourfolds

Abstract

The present paper proves that finite symplectic groups of automorphisms of hyperk\"ahler fourfolds deformation equivalent to the Hilbert scheme of two points on a $K3$ surface are contained in the simple group $Co_1$. Then we give an example of a symplectic automorphism of order 11 on the Fano scheme of lines of a cubic fourfold.