Surfaces violating Bogomolov-Miyaoka-Yau in positive characteristic

Easton, Robert

doi:10.1090/S0002-9939-08-09466-5

Surfaces violating Bogomolov-Miyaoka-Yau in positive characteristic
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by Robert W. Easton PDF

Proc. Amer. Math. Soc. 136 (2008), 2271-2278 Request permission

Abstract:

The Bogomolov-Miyaoka-Yau inequality asserts that the Chern numbers of a surface $X$ of general type in characteristic 0 satisfy the inequality $c_1^2\leq 3c_2$, a consequence of which is $\frac {K_X^2}{\chi ({\mathcal O}_X)}\leq 9$. This inequality fails in characteristic $p$, and here we produce infinite families of counterexamples for large $p$. Our method parallels a construction of Hirzebruch, and relies on a construction of abelian covers due to Catanese and Pardini.

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