2016/12/24 by Atanas Iliev, Iliev, Atanas, Laurent Manivel +1 · 1 citation
Mathematics · #14J28 #14J45 #14M15 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14J28 #msc:14J45 #msc:14M15
paper · pdf · doi:10.48550/arxiv.1612.08173
arxiv created 2016/12/24 · arxiv updated 2016/12/28
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.