Hyperkahler manifolds from the Tits-Freudenthal square
Algebraic Geometry
2016-12-28 v1
Abstract
We suggest a way to associate to each Lie algebra of type G2, D4, F4, E6, E7, E8 a family of polarized hyperkahler fourfolds, constructed as parametrizing certain families of cycles of hyperplane sections of certain homogeneous or quasi-homogeneous varieties. These cycles are modeled on the Legendrian varieties studied by Freudenthal in his geometric approach to the celebrated Tits-Freudenthal magic square of Lie algebras.
Keywords
Cite
@article{arxiv.1612.08173,
title = {Hyperkahler manifolds from the Tits-Freudenthal square},
author = {Atanas Iliev and Laurent Manivel},
journal= {arXiv preprint arXiv:1612.08173},
year = {2016}
}