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

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

2000-03-31

arxiv.org/abs/math/0003230v1

Mathematics

Algebraic Geometry

10 pages, LaTeX

Scientific paper

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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