# Toric Fano varieties and birational morphisms

@article{Casagrande2001ToricFV,
title={Toric Fano varieties and birational morphisms},
author={Cinzia Casagrande},
journal={International Mathematics Research Notices},
year={2001},
volume={2003},
pages={1473-1505}
}
• C. Casagrande
• Published 1 December 2001
• Mathematics
• International Mathematics Research Notices
In this paper we study smooth toric Fano varieties using primitive relations and toric Mori theory. We show that for any irreducible invariant divisor D in a toric Fano variety X, we have $0\leq\rho_X-\rho_D\leq 3$, for the difference of the Picard numbers of X and D. Moreover, if $\rho_X-\rho_D>0$ (with some additional hypotheses if $\rho_X-\rho_D=1$), we give an explicit birational description of X. Using this result, we show that when dim X=5, we have $\rho_X\leq 9$. In the second part of…
20 Citations

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