English

Manifolds of low dimension with trivial canonical bundle in Grassmannians

Algebraic Geometry 2017-05-30 v3

Abstract

We study fourfolds with trivial canonical bundle which are zero loci of sections of homogeneous, completely reducible bundles over ordinary and classical complex Grassmannians. We prove that the only HyperK{\"a}hler fourfolds among them are the example of Beauville and Donagi, and the example of Debarre and Voisin. In doing so, we give a complete classification of those varieties. We include also the analogous classification for surfaces and threefolds.

Keywords

Cite

@article{arxiv.1609.02695,
  title  = {Manifolds of low dimension with trivial canonical bundle in Grassmannians},
  author = {Vladimiro Benedetti},
  journal= {arXiv preprint arXiv:1609.02695},
  year   = {2017}
}