The group of Cremona transformations generated by linear maps and the standard involution

[Le groupe des transformations de Cremona engendré par les applications linéaires et l’involution standard]

Blanc, Jérémy ; Hedén, Isac

Annales de l'Institut Fourier, Tome 65 (2015), p. 2641-2680 / Harvested from Numdam

Résumé

Cet article étudie le groupe engendré par les automorphismes de l’espace projectif de dimension $n$ et par l’involution birationnelle standard de degré $n$. Tout élément de ce groupe ne contracte que des hypersurfaces rationnelles, mais en dimension impaire il existe des éléments simples qui ont cette propriété et n’appartiennent pas au groupe. Des propriétés géométriques du groupe sont données, de même qu’une description de son intersection avec le groupe des transformations monômiales.

Abstract

This article studies the group generated by automorphisms of the projective space of dimension $n$ and by the standard birational involution of degree $n$. Every element of this group only contracts rational hypersurfaces, but in odd dimension, there are simple elements having this property which do not belong to the group. Geometric properties of the elements of the group are given, as well as a description of its intersection with monomial transformations.

Détail

Publié le : 2015-01-01
DOI : https://doi.org/10.5802/aif.2999
Classification:  14E07
Mots clés: Transformations de Cremona, involution standard, hypersurfaces rationnelles, transformations monômiales

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