On the inertia group of elliptic curves in the Cremona group of the plane

Blanc, Jérémy. (2008) On the inertia group of elliptic curves in the Cremona group of the plane. >>The<< Michigan mathematical journal, Vol. 56, H. 2. pp. 315-330.

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Official URL: http://edoc.unibas.ch/dok/A5843080

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We study the group of birational transformations of the plane that fix (each point of) a curve of geometric genus 1. A precise description of the finite elements is given; it is shown in particular that the order is at most 6, and that if the group contains a non-trivial torsion, the fixed curve is the image of a smooth cubic by a birational transformation of the plane. We show that for a smooth cubic, the group is generated by its elements of degree 3, and prove that it contains a free product of Z/2Z, indexed by the points of the curve.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Algebra (Blanc)
UniBasel Contributors:Blanc, Jérémy
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:University of Michigan Press
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:08 Jun 2012 06:56
Deposited On:08 Jun 2012 06:47

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