Triangulations and Severi Varieties

Abstract

We consider the problem of constructing triangulations of projective planes over Hurwitz algebras with minimal numbers of vertices. We observe that the numbers of faces of each dimension must be equal to the dimensions of certain representations of the automorphism groups of the corresponding Severi varieties. We construct a complex involving these representations, which should be considered a geometric version of the (putative) triangulations.

2000 AMS Subject Classification:

• 13F55
• 55U10
• 17A35
• 51E15
• 14M17

Keywords:

• Severi variety
• Hurwitz algebra
• projective plane
• simplicial manifold
• triangulation

Notes

¹LiE is available at http://young.sp2mi.univ-poitiers.fr/marc/LiE/ .