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On planar Cremona maps of prime order

Published online by Cambridge University Press:  22 January 2016

Tommaso de Fernex
Tommaso de Fernex*
Affiliation:
Department of Mathematics, University of Michigan, East Hall, 525 East University Avenue, Ann Arbor, MI 48109-1109, USA, defernex@umich.edu
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Abstract

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This paper contains a new proof of the classification of prime order elements of Bir(ℙ2) up to conjugation. The first results on this topic can be traced back to classic works by Bertini and Kantor, among others. The innovation introduced by this paper consists of explicit geometric constructions of these Cremona transformations and the parameterization of their conjugacy classes. The methods employed here are inspired to [4], and rely on the reduction of the problem to classifying prime order automorphisms of rational surfaces. This classification is completed by combining equivariant Mori theory to the analysis of the action on anticanonical rings, which leads to characterize the cases that occur by explicit equations (see [28] for a different approach). Analogous constructions in higher dimensions are also discussed.

Keywords

14E0714J5014E20
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 174 , 2004 , pp. 1 - 28
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2004

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