Quasi elementary contractions of Fano manifolds
| dc.creator | Casagrande, C. | |
| dc.date | 2007-04-30 | |
| dc.date | 2008-04-18 | |
| dc.date.accessioned | 2026-07-07T09:33:01Z | |
| dc.date.available | 2026-07-07T09:33:01Z | |
| dc.description | Let X be a smooth complex Fano variety. We define and study 'quasi elementary' contractions of fiber type f: X -> Y. These have the property that rho(X) is at most rho(Y)+rho(F), where rho is the Picard number and F is a general fiber of f. In particular any elementary extremal contraction of fiber type is quasi elementary. We show that if Y has dimension at most 3 and Picard number at least 4, then Y is smooth and Fano; if moreover rho(Y) is at least 6, then X is a product. This yields sharp bounds on rho(X) when dim(X)=4 and X has a quasi elementary contraction, and other applications in higher dimensions. | |
| dc.description | Final version, minor changes, to appear in Compositio Mathematica | |
| dc.identifier | https://arxiv.org/abs/0704.3912 | |
| dc.identifier | http://arxiv.org/abs/0704.3912 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158991 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14J45, 14E30 | |
| dc.title | Quasi elementary contractions of Fano manifolds | |
| dc.type | text |