# 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} }

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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