Triangulations and Severi varieties

Frédéric Chapoton (1) , Laurent Manivel (2)

1 ICJ - Institut Camille Jordan
2 IF - Institut Fourier

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 as a geometric version of the (putative) triangulations.

Mots clés: triangulation; Hurwitz algebra; projective plane; Severi variety; Hasse diagram; Jordan algebra; Koszul complex

Domaines: Géométrie algébrique [math.AG]; Topologie algébrique [math.AT]; Théorie des représentations [math.RT]; Combinatoire [math.CO]

Frédéric Chapoton, Laurent Manivel. Triangulations and Severi varieties. Experimental Mathematics, 2013, 22 (1), pp.60-73. ⟨10.1080/10586458.2013.743854⟩. ⟨hal-00627570⟩