The real plane Cremona group is an amalgamated product
نویسندگان
چکیده
We show that the real Cremona group of plane is a non-trivial amalgam two groups amalgamated along their intersection and give an alternative proof its abelianisation.
منابع مشابه
The Cremona group of the plane is compactly presented
This article shows that the Cremona group of the plane is compactly presented. To do this we prove that it is a generalised amalgamated product of three of its algebraic subgroups (automorphisms of the plane and Hirzebruch surfaces) divided by one relation.
متن کاملAppendix A . The Cremona group is not an amalgam Yves
Let k be a field. The Cremona group Bir(Pk) of k in dimension d is defined as the group of birational transformations of the d-dimensional k-affine space. It can also be described as the group of k-automorphisms of the field of rational functions k(t1, . . . , td). We endow it with the discrete topology. Let us say that a group has Property (FR)∞ if it satisfies the following (1) For every isom...
متن کاملThe Cremona group of the plane is compactly presented Susanna Zimmermann
This article shows that the Cremona group of the plane is compactly presented. To do this, we prove that it is a generalized amalgamated product of three of its algebraic subgroups (automorphisms of the plane and Hirzebruch surfaces) divided by one relation.
متن کاملOn the Inertia Group of Elliptic Curves in the Cremona Group of the Plane
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 smoot...
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ژورنال
عنوان ژورنال: Annales de l'Institut Fourier
سال: 2021
ISSN: ['0373-0956', '1777-5310']
DOI: https://doi.org/10.5802/aif.3415