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On algebraic surfaces of general type with negative $c_{2}$

Part of: Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  22 June 2016

Yi Gu
Yi Gu*
Affiliation:
Peking University, 5, Yiheyuan Road, Beijing, China email pkuguyi2010@gmail.com, Yi.Gu@math.u-bordeaux1.fr Institut de Mathématiques de Bordeaux, Université de Bordeaux, 351, Cours de la Libération, 33405 Talence, France
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Abstract

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We prove that for any prime number $p\geqslant 3$, there exists a positive number $\unicode[STIX]{x1D705}_{p}$ such that $\unicode[STIX]{x1D712}({\mathcal{O}}_{X})\geqslant \unicode[STIX]{x1D705}_{p}c_{1}^{2}$ holds true for all algebraic surfaces $X$ of general type in characteristic $p$. In particular, $\unicode[STIX]{x1D712}({\mathcal{O}}_{X})>0$. This answers a question of Shepherd-Barron when $p\geqslant 3$.

Keywords

Euler characteristicssurfaces of general type

MSC classification

Primary: 14J29: Surfaces of general type
Type
Research Article
Information
Compositio Mathematica , Volume 152 , Issue 9 , September 2016 , pp. 1966 - 1998
Copyright
© The Author 2016 

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