On numerically trivial automorphisms of compact hyperk\"ahler manifolds of dimension 4

TL;DR

This paper proves that for 4-dimensional compact hyperk"ahler manifolds, every automorphism acts non-trivially on the cohomology ring, establishing a faithful action.

Contribution

It demonstrates that the automorphism group of such manifolds acts faithfully on their cohomology ring, a new result in hyperk"ahler geometry.

Findings

Automorphism group acts faithfully on cohomology

Faithfulness holds specifically in dimension 4

Advances understanding of symmetries in hyperk"ahler manifolds

Abstract

We prove that the automorphism group of a compact hyperk\"ahler manifold of dimension 4 acts faithfully on the cohomology ring.