Monodromy Invariants and Polarization Types of Generalized Kummer Fibrations

TL;DR

This paper constructs a monodromy invariant for isotropic classes on generalized Kummer manifolds and uses it to determine the polarization types of Lagrangian fibrations, revealing their dependence on moduli space components.

Contribution

It introduces a new monodromy invariant for isotropic classes and applies it to classify polarization types of Lagrangian fibrations on generalized Kummer manifolds.

Findings

Polarization type depends on the connected component of the moduli space.

A monodromy invariant for isotropic classes is constructed.

The invariant helps determine the polarization type of fibrations.

Abstract

In this paper a monodromy invariant for isotropic classes on generalized Kummer type manifolds is constructed. This invariant is used to determine the polarization type of Lagrangian fibrations on such manifolds - a notion which was introduced in an earlier paper of the author. The result shows that the polarization type of a Lagrangian fibration of generalized Kummer type depends on the connected component of the moduli space.