Monodromy Invariants and Polarization Types of Generalized Kummer 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.

This is the final version of the paper. Some improvements, thanks to the referee. The paper was published in Mathematische Zeitschrift. Please note that my Leibniz Universität email address (@math.uni-hannover.de) does not work anymore, Math. Z. (2018)

References in corpus (4)

• Base manifolds for fibrations of projective irreducible symplectic manifolds
• On isotropic divisors on irreducible symplectic manifolds
• Base manifolds for Lagrangian fibrations on hyperkähler manifolds
• On polarization types of Lagrangian fibrations

Cited by in corpus (4)

• Symplectic involutions of $K{3}^{[n]}$ type and Kummer $n$ type manifolds
• On the image of the period map for polarized hyperkähler manifolds
• Singular fibres of very general Lagrangian fibrations
• Sixfolds of generalized Kummer type and K3 surfaces