Hyperkähler manifolds from the Tits–Freudenthal magic square

Atanas Iliev (1) , Laurent Manivel (2)

1 Department of Mathematics
2 IMT - Institut de Mathématiques de Toulouse UMR5219

We suggest a way to associate to each Lie algebra of type G 2 , D 4 , F 4 , E 6 , E 7 , E 8 a family of polarized hyperkähler 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.

Domaines: Mathématiques [math]; Géométrie algébrique [math.AG]

Atanas Iliev, Laurent Manivel. Hyperkähler manifolds from the Tits–Freudenthal magic square. Central European Journal of Mathematics, 2019. ⟨hal-01974883⟩