On the Picard number of singular Fano varieties
Algebraic Geometry
2012-12-05 v1
Abstract
Let X be a Q-factorial Gorenstein Fano variety. Suppose that the singularities of X are canonical and that the locus where they are non-terminal has dimension zero. Let D be a prime divisor of X. We show that rho_X - rho_D < 9 (where rho is the Picard number). Moreover, if rho_X - rho_D > 3, there exists a finite morphism from X to S x Y, where S is a surface with rho_S at most 9. As an application we prove that, if X has dimension 3, then rho_X is at most 10.
Keywords
Cite
@article{arxiv.1202.1154,
title = {On the Picard number of singular Fano varieties},
author = {Gloria Della Noce},
journal= {arXiv preprint arXiv:1202.1154},
year = {2012}
}
Comments
arXiv admin note: text overlap with arXiv:0905.3239