Toric Fano varieties and birational morphisms
| dc.creator | Casagrande, Cinzia | |
| dc.date | 2001-12-01 | |
| dc.date.accessioned | 2026-07-07T04:44:56Z | |
| dc.date.available | 2026-07-07T04:44:56Z | |
| dc.description | 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 $0\leqρ_X-ρ_D\leq 3$, for the difference of the Picard numbers of X and D. Moreover, if $ρ_X-ρ_D>0$ (with some additional hypotheses if $ρ_X-ρ_D=1$), we give an explicit birational description of X. Using this result, we show that when dim X=5, we have $ρ_X\leq 9$. In the second part of the paper, we study equivariant birational morphisms f whose source is Fano. We give some general results, and in dimension 4 we show that f is always a composite of smooth equivariant blow-ups. Finally, we study under which hypotheses a non-projective toric variety can become Fano after a smooth equivariant blow-up. | |
| dc.description | LaTeX, 35 pages, 27 figures, 2 tables | |
| dc.identifier | https://arxiv.org/abs/math/0112007 | |
| dc.identifier | http://arxiv.org/abs/math/0112007 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62791 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Toric Fano varieties and birational morphisms | |
| dc.type | text |