English

Surfaces Violating Bogomolov-Miyaoka-Yau in Positive Characteristic

Algebraic Geometry 2007-05-23 v1

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 <= 3c_2, a consequence of which is (K_X^2)/chi(O_X) <= 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.

Keywords

Cite

@article{arxiv.math/0511455,
  title  = {Surfaces Violating Bogomolov-Miyaoka-Yau in Positive Characteristic},
  author = {Robert Easton},
  journal= {arXiv preprint arXiv:math/0511455},
  year   = {2007}
}

Comments

10 pages