Surfaces Violating Bogomolov-Miyaoka-Yau in Positive Characteristic
Abstract
The Bogomolov-Miyaoka-Yau inequality asserts that the Chern numbers of a surface X of general type in characteristic 0 satisfy the inequality c12 <= 3c2, a consequence of which is (KX2)/chi(OX) <= 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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