Fundamental divisors on Fano varieties of index n-3

Details Fundamental divisors on Fano varieties of index n-3 Fundamental divisors on Fano varieties of index n-3

2010-09-04

arxiv.org/abs/1009.0812v2

Mathematics

Algebraic Geometry

Scientific paper

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.

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