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Algebraic Surfaces of General Type with Small c21 in Positive Characteristic

Published online by Cambridge University Press:  11 January 2016

Christian Liedtke
Christian Liedtke*
Affiliation:
Mathematisches Institut, Heinrich-Heine-Universität, 40225 Düsseldorf, Germany, liedtke@math.uni-duesseldorf.de
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Abstract

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We establish Noether’s inequality for surfaces of general type in positive characteristic. Then we extend Enriques’ and Horikawa’s classification of surfaces on the Noether line, the so-called Horikawa surfaces. We construct examples for all possible numerical invariants and in arbitrary characteristic, where we need foliations and deformation techniques to handle characteristic 2. Finally, we show that Horikawa surfaces lift to characteristic zero.

Keywords

14J2914J10
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 191 , 2008 , pp. 111 - 134
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2008

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