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Characterizations of ${\mathbb P}^n$ in arbitrary characteristic

Yasuyuki Kachi·János Kollár
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Abstract

We prove that a smooth projective variety of dimension n is isomorphic to projective n-space iff the canonical class is -(n+1)-times an ample divisor. In characteristic zero this was proved by Kobayashi-Ochiai. We also extend the second adjunction theorem of Ionescu and Fujita to arbitrary characteristic.

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Yasuyuki Kachi, János Kollár. 2000-03-31. Characterizations of ${\mathbb P}^n$ in arbitrary characteristic. https://arxiv.org/abs/math/0003230

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