Symmetric differential forms on complete intersection varieties and applications

Damian Brotbek (1)

1 IRMA - Institut de Recherche Mathématique Avancée

In this paper we study the cohomology of tensor products of symmetric powers of the cotangent bundle of complete intersection varieties in projective space. We provide an explicit description of some of those cohomology groups in terms of the equations defining the complete intersection. We give several applications. First we prove a non-vanishing result, then we give a new example illustrating the fact that the dimension of the space of holomorphic symmetric differential forms is not deformation invariant. Our main application is the construction of varieties with ample cotangent bundle, providing new results towards a conjecture of Debarre.

Mots clés: symmetric differential forms; ample cotangent bundle; symmetric differential forms.

Domaines: Géométrie algébrique [math.AG]

Damian Brotbek. Symmetric differential forms on complete intersection varieties and applications. Mathematische Annalen, 2016, 366, pp.417-446. ⟨10.1007/s00208-015-1332-7⟩. ⟨hal-01016306⟩