Lagrangian fibrations on generalized Kummer varieties
Algebraic Geometry
2011-04-27 v1
Abstract
We investigate the existence of Lagrangian fibrations on the generalized Kummer varieties of Beauville. For a principally polarized abelian surface A of Picard number one we find the following: The Kummer variety K^n(A) is birationally equivalent to another irreducible symplectic variety admitting a Lagrangian fibration, if and only if n is a perfect square. And this is the case if and only if K^n(A) carries a divisor with vanishing Beauville-Bogomolov square.
Keywords
Cite
@article{arxiv.math/0510145,
title = {Lagrangian fibrations on generalized Kummer varieties},
author = {Martin G. Gulbrandsen},
journal= {arXiv preprint arXiv:math/0510145},
year = {2011}
}
Comments
13 pages