Chapitre D'ouvrage Année : 2013

Acyclic curves and group actions on affine toric surfaces

Résumé

We show that every irreducible, simply connected curve on a toric affine surface $X$ over $\CC$ is an orbit closure of a $\G_m$-action on $X$. It follows that up to the action of the automorphism group $\Aut(X)$ there are only finitely many non-equivalent embeddings of the affine line $Å^1$ in $X$. A similar description is given for simply connected curves in the quotients of the affine plane by small finite linear groups. We provide also an analog of the Jung-van der Kulk theorem for affine toric surfaces, and apply this to study actions of algebraic groups on such surfaces.

Fichier principal
Vignette du fichier
Acyclic_curves_on_toric_surfaces.pdf (391.38 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence

Dates et versions

hal-00632263 , version 1 (13-10-2011)

Licence

Identifiants

Citer

Ivan Arzhantsev, Mikhail Zaidenberg. Acyclic curves and group actions on affine toric surfaces. Kayo Masuda, Hideo Kojima, Takashi Kishimoto (eds.). Affine Algebraic Geometry, World Scientific Publiching Co. pp.1-41, 2013, Proceedings of the Conference Osaka, Japan, 3 – 6 March 2011, 978-981-4436-71-7 ⟨10.1142/9789814436700_0001⟩. ⟨hal-00632263⟩
130 Consultations
297 Téléchargements

Altmetric

Partager

  • More