On subgroups of an automorphism group of an irreducible symplectic manifold

TL;DR

This paper investigates the structure of automorphism subgroups fixing a nef isotropic line bundle on an irreducible symplectic manifold, providing a formula for their rank and insights into the nef cone structure.

Contribution

It introduces a formula for the rank of Aut(X,L) using MBM divisors and generalizes Kovac's nef cone theorem to higher-dimensional symplectic manifolds.

Findings

Formula for the rank of Aut(X,L) in terms of MBM divisors

Nef cone of X is cut out by MBM classes

Generalization of Kovac's nef cone structure theorem

Abstract

Let X be an irreducible symplectic manifold and L a nef line bundle on X which is isotropic with respect to the Beauville-Bogomolov quadratic form. It is known that a subgroup Aut(X,L) of an automorphism group of X which fix L is almost abelian. We give a formula of the rank of Aut(X,L) in terms of MBM divisors. We also prove that the nef cone of X cut out MBM classes, which is a generalization of Kovac's structure theorem of nef cones of K3 surfaces