Advanced Studies in Pure Mathematics

Numerical characterisations of hyperquadrics

Yoichi Miyaoka

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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 $X$.

Article information

Source
Complex Analysis in Several Variables — Memorial Conference of Kiyoshi Oka's Centennial Birthday, Kyoto/Nara 2001, K. Miyajima, M. Furushima, H. Kazama, A. Kodama, J. Noguchi, T. Ohsawa, H. Tsuji and T. Ueda, eds. (Tokyo: Mathematical Society of Japan, 2004), 209-235

Dates
Received: 22 August 2002
First available in Project Euclid: 3 January 2019

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1546542852

Digital Object Identifier
doi:10.2969/aspm/04210209

Mathematical Reviews number (MathSciNet)
MR2087053

Zentralblatt MATH identifier
1063.14050

Citation

Miyaoka, Yoichi. Numerical characterisations of hyperquadrics. Complex Analysis in Several Variables — Memorial Conference of Kiyoshi Oka's Centennial Birthday, Kyoto/Nara 2001, 209--235, Mathematical Society of Japan, Tokyo, Japan, 2004. doi:10.2969/aspm/04210209. https://projecteuclid.org/euclid.aspm/1546542852


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