Quasi-complete homogeneous contact manifold associated to a cubic form

Jun-Muk Hwang (1) , Laurent Manivel (2)

1 KIAS - Korea Institute for Advanced Study
2 IF - Institut Fourier

Starting from a cubic form, we give a general construction of a quasi-complete homogeneous manifold endowed with a natural contact structure. We show that it can be compactified into a projective contact manifold if and only if the cubic form is the determinant of a simple cubic Jordan algebra.

Mots clés: cubic form; Jordan algebra; contact manifold; homogeneous variety; rational curve

Domaines: Géométrie algébrique [math.AG]

Jun-Muk Hwang, Laurent Manivel. Quasi-complete homogeneous contact manifold associated to a cubic form. Contemporary mathematics, 2010, Vector bundles and complex geometry, 522, pp.105-112. ⟨hal-00348541⟩