Surfaces violating Bogomolov-Miyaoka-Yau in positive characteristic

Author:
Robert W. Easton

Journal:
Proc. Amer. Math. Soc. **136** (2008), 2271-2278

MSC (2000):
Primary 14J29

DOI:
https://doi.org/10.1090/S0002-9939-08-09466-5

Published electronically:
March 6, 2008

MathSciNet review:
2390492

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Abstract: The Bogomolov-Miyaoka-Yau inequality asserts that the Chern numbers of a surface of general type in characteristic 0 satisfy the inequality , a consequence of which is . This inequality fails in characteristic , and here we produce infinite families of counterexamples for large . Our method parallels a construction of Hirzebruch, and relies on a construction of abelian covers due to Catanese and Pardini.

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Additional Information

**Robert W. Easton**

Affiliation:
Department of Mathematics, University of Utah, Salt Lake City, Utah 84102

Email:
easton@math.utah.edu

DOI:
https://doi.org/10.1090/S0002-9939-08-09466-5

Keywords:
Bogomolov inequality,
abelian cover,
positive characteristic,
algebraic surface,
general type

Received by editor(s):
December 6, 2005

Published electronically:
March 6, 2008

Communicated by:
Ted Chinburg

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.