• DOI:10.1093/imrn/rns236
Corpus ID: 119641699

On the Picard number of singular Fano varieties

@article{Noce2012OnTP,
  title={On the Picard number of singular Fano varieties},
  author={Gloria Della Noce},
  journal={arXiv: Algebraic Geometry},
  year={2012}
}

• Gloria Della Noce
• Published 2012
• Mathematics
• arXiv: Algebraic Geometry

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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 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.