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ENRIQUES’ CLASSIFICATION IN CHARACTERISTIC $p>0$: THE $P_{12}$-THEOREM

Part of: Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  27 February 2018

FABRIZIO CATANESE  and
BINRU LI
FABRIZIO CATANESE
Affiliation:
Lehrstuhl Mathematik VIII, Mathematisches Institut der Universität Bayreuth, NW II, Universitätsstr. 30, 95447 Bayreuth, Germany email Fabrizio.Catanese@uni-bayreuth.de
BINRU LI
Affiliation:
Lehrstuhl Mathematik VIII, Mathematisches Institut der Universität Bayreuth, NW II, Universitätsstr. 30, 95447 Bayreuth, Germany email Binru.Li@uni-bayreuth.de
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Abstract

The main goal of this paper is to show that Castelnuovo–Enriques’ $P_{12}$- theorem (a precise version of the rough classification of algebraic surfaces) also holds for algebraic surfaces $S$ defined over an algebraically closed field $k$ of positive characteristic ($\text{char}(k)=p>0$). The result relies on a main theorem describing the growth of the plurigenera for properly elliptic or properly quasielliptic surfaces (surfaces with Kodaira dimension equal to 1). We also discuss the limit cases, i.e., the families of surfaces which show that the result of the main theorem is sharp.

MSC classification

Primary: 14J10: Families, moduli, classification 14J27: Elliptic surfaces
Type
Article
Information
Nagoya Mathematical Journal , Volume 235 , September 2019 , pp. 201 - 226
Copyright
© 2018 Foundation Nagoya Mathematical Journal  

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Footnotes

The present work took place in the framework of the ERC Advanced grant no. 340258, “TADMICAMT.”

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