Surfaces violating Bogomolov-Miyaoka-Yau in positive characteristic
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- by Robert W. Easton
- Proc. Amer. Math. Soc. 136 (2008), 2271-2278
- DOI: https://doi.org/10.1090/S0002-9939-08-09466-5
- Published electronically: 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.References
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Bibliographic Information
- Robert W. Easton
- Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84102
- Email: easton@math.utah.edu
- Received by editor(s): December 6, 2005
- Published electronically: March 6, 2008
- Communicated by: Ted Chinburg
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 2271-2278
- MSC (2000): Primary 14J29
- DOI: https://doi.org/10.1090/S0002-9939-08-09466-5
- MathSciNet review: 2390492