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Hyperkahler manifolds from the Tits-Freudenthal square

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.

preprint2016arXivOpen access
Atanas IlievLaurent Manivel
math.AG
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Atanas IlievLaurent Manivel

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