Lagrangian fibrations on hyperk\"ahler fourfolds
Algebraic Geometry
2015-04-17 v3
Abstract
Let X be a projective hyperk\"ahler manifold containing a Lagrangian subtorus L. We study intersections of deformations of L, defining a canonical almost holomorphic map called L-reduction, which is not birational if and only if X admits an almost holomorphic Lagrangian fibration with (strong) fibre L. In dimension four we prove that in the above situation there is always a holomorphic Lagrangian fibration with fibre L, thus answering a question of Beauville in this particular case.
Cite
@article{arxiv.1110.2680,
title = {Lagrangian fibrations on hyperk\"ahler fourfolds},
author = {Daniel Greb and Christian Lehn and Sönke Rollenske},
journal= {arXiv preprint arXiv:1110.2680},
year = {2015}
}
Comments
10 pages, 1 figure; v2: added reference to arXiv:1110.2852; v3: exposition improved, bibliography updated, to appear in Izvestiya: Mathematics