A remark on Fano 4-folds having (3,1)-type extremal contractions |
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Authors: | Toru Tsukioka |
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Institution: | 1. Faculty of Liberal Arts and Sciences, Osaka Prefecture University, 1-1 Gakuen-cho, Nakaku, Sakai, Osaka, 599-8531, Japan
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Abstract: | Let π : X → Y be the blow-up of a four-dimensional complex manifold Y along a smooth curve C. Assume that X is a Fano manifold and has another (3,1)-type extremal contraction ${\varphi : X \to Z}$ whose exceptional divisor meet that of the blow-up π : X → Y. We show that if the exceptional divisor of ${\varphi}$ is smooth, then Y is isomorphic to four-dimensional projective space and C is an elliptic curve of degree 4. |
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