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VOL. 42 | 2004 Numerical characterisations of hyperquadrics
Yoichi Miyaoka

Editor(s) Kimio Miyajima, Mikio Furushima, Hideaki Kazama, Akio Kodama, Junjiro Noguchi, Takeo Ohsawa, Hajime Tsuji, Tetsuo Ueda

Abstract

Smooth quadric hypersuraces in $\mathbb{P}^{n+1} (\mathbb{C})$ are numerically characterised as the smooth Fano $n$-folds of length $n$, i.e., a smooth Fano $n$-fold $X$ is isomorphic to a hyperquadric if and only if the minimum of the intersection number $(C, -K_X)$ is $n$, where $C$ runs through the rational curves on $X$.

Information

Published: 1 January 2004
First available in Project Euclid: 3 January 2019

zbMATH: 1063.14050
MathSciNet: MR2087053

Digital Object Identifier: 10.2969/aspm/04210209

Rights: Copyright © 2004 Mathematical Society of Japan

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