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2004 On planar Cremona maps of prime order
Tommaso de Fernex
Nagoya Math. J. 174: 1-28 (2004).


This paper contains a new proof of the classification of prime order elements of $\Bir(\P^2)$ 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.


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Tommaso de Fernex. "On planar Cremona maps of prime order." Nagoya Math. J. 174 1 - 28, 2004.


Published: 2004
First available in Project Euclid: 27 April 2005

zbMATH: 1062.14019
MathSciNet: MR2066103

Primary: 14E07

Rights: Copyright © 2004 Editorial Board, Nagoya Mathematical Journal


Vol.174 • 2004
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