On the monodromy of irreducible symplectic manifolds

TL;DR

This paper investigates the monodromy groups of irreducible symplectic manifolds, providing new computations for generalized Kummer manifolds and showing the monodromy of O'Grady's 10-dimensional manifold is smaller than previously thought.

Contribution

It offers a novel approach to computing monodromy groups using recent results on the ample cone, completing the monodromy group calculation for generalized Kummer manifolds and refining understanding for O'Grady's manifold.

Findings

Monodromy group for generalized Kummer manifolds fully computed.

Monodromy of O'Grady's 10-dimensional manifold is smaller than expected.

Provides a new perspective on monodromy computation using ample cone results.

Abstract

Exploiting recent results on the ample cone of irreducible symplectic manifolds, we provide a different point of view for the computation of their monodromy groups. In particular, we give the final step in the computation of the monodromy group for generalised Kummer manifolds and we prove that the monodromy of O'Grady's ten dimensional manifold is smaller than what was expected.