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Surfaces violating Bogomolov-Miyaoka-Yau in positive characteristic

Author(s): Robert W. Easton
Journal: Proc. Amer. Math. Soc. 136 (2008), 2271-2278.
MSC (2000): Primary 14J29
Posted: March 6, 2008
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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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Additional Information:

Robert W. Easton
Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84102
Email: easton@math.utah.edu

DOI: 10.1090/S0002-9939-08-09466-5
PII: S 0002-9939(08)09466-5
Keywords: Bogomolov inequality, abelian cover, positive characteristic, algebraic surface, general type
Received by editor(s): December 6, 2005
Posted: March 6, 2008
Communicated by: Ted Chinburg
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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