Affine lines in the complement of a smooth plane conic - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Bollettino dell'Unione Matematica Italiana Année : 2018

Affine lines in the complement of a smooth plane conic

Résumé

We classify closed curves isomorphic to the affine line in the complement of a smooth rational projective plane conic $Q$. Over a field of characteristic zero, we show that up to the action of the subgroup of the Cremona group of the plane consisting of birational endomorphisms restricting to biregular automorphisms outside $Q$, there are exactly two such lines: the restriction of a smooth conic osculating $Q$ at a rational point and the restriction of the tangent line to $Q$ at a rational point. In contrast, we give examples illustrating the fact that over fields of positive characteristic, there exist exotic closed embeddings of the affine line in the complement of $Q$. We also determine an explicit set of birational endomorphisms of the plane whose restrictions generates the automorphism group of the complement of $Q$ over a field of arbitrary characteristic.
Fichier principal
Vignette du fichier
AM-Quadric.pdf (252.93 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01394595 , version 1 (09-11-2016)

Identifiants

Citer

Julie Decaup, Adrien Dubouloz. Affine lines in the complement of a smooth plane conic. Bollettino dell'Unione Matematica Italiana, 2018, 11 (1), pp.39-54. ⟨10.1007/s40574-017-0119-z⟩. ⟨hal-01394595⟩
132 Consultations
190 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More