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arXiv · 1612.08173

Hyperkahler manifolds from the Tits-Freudenthal square

Atanas Iliev·Laurent Manivel
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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.

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Atanas Iliev, Laurent Manivel. 2016-12-24. Hyperkahler manifolds from the Tits-Freudenthal square. https://arxiv.org/abs/1612.08173

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