2007/03/31 by Jérémy Blanc
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory #Elliptic curve #Genus #Geometry #Group (periodic table) #Mathematics #Order (exchange) #Physics #Plane (geometry) #Plane curve #Polynomial and algebraic computation #Pure mathematics #Quartic plane curve #Torsion (gastropod) #math.AG #msc:14E05 #msc:14E07 #msc:14H52
paper · pdf · doi:10.1307/mmj/1224783516
published as Michigan Math. J. 56 (2008), no. 2, 315-330. · 14 pages, no figure
arxiv created 2007/10/23 · openalex publication_date 2008/10/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract. 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 the embedding of the fixed curve in P 2 need to be birationally equivalent to a plane smooth cubic. 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. 1.