A remark on Fano 4-folds having (3,1)-type extremal contractions

dc.creatorTsukioka, Toru
dc.date2007-10-09
dc.date.accessioned2026-07-07T08:35:00Z
dc.date.available2026-07-07T08:35:00Z
dc.descriptionLet 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.description8 pages
dc.identifierhttps://arxiv.org/abs/0710.1719
dc.identifierhttp://arxiv.org/abs/0710.1719
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/139629
dc.subjectAlgebraic Geometry
dc.subject14J45; 14E30
dc.titleA remark on Fano 4-folds having (3,1)-type extremal contractions
dc.typetext

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