A remark on Fano 4-folds having (3,1)-type extremal contractions
| dc.creator | Tsukioka, Toru | |
| dc.date | 2007-10-09 | |
| dc.date.accessioned | 2026-07-07T08:35:00Z | |
| dc.date.available | 2026-07-07T08:35:00Z | |
| dc.description | Let X be the blow-up of a smooth projective 4-fold Y along a smooth curve C and let E be the exceptional divisor. Assume that X is a Fano manifold and has an elementary extremal contraction $ϕ: X \to Z$ of (3,1)-type such that E is $ϕ$-ample (recall that a contraction map for a 4-fold is called (3,1)-type if the exceptional locus is a divisor and its image is a curve). We show that if the exceptional divisor of $ϕ$ is smooth, then Y is isomorphic to $\mathbb{P}^{4}$ and C is an elliptic curve of degree 4. | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/0710.1719 | |
| dc.identifier | http://arxiv.org/abs/0710.1719 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/139629 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14J45; 14E30 | |
| dc.title | A remark on Fano 4-folds having (3,1)-type extremal contractions | |
| dc.type | text |