Fundamental divisors on Fano varieties of index n − 3

Enrica Floris (1)

1 IRMA - Institut de Recherche Mathématique Avancée

Let X be a Fano manifold of dimension n and index n − 3. Kawamata proved the non vanishing of the global sections of the fundamental divisor in the case n = 4. Moreover he proved that if Y is a general element of the fundamental system then Y has at most canonical singularities. We prove a generalization of this result in arbitrary dimension.

Domains: Algebraic Geometry [math.AG]

Enrica Floris. Fundamental divisors on Fano varieties of index n − 3. Geometriae Dedicata, 2013, ⟨10.1007/s10711-012-9713-5⟩. ⟨hal-01280959⟩