AUTOMORPHISM GROUPS OF CONFIGURATION SPACES AND DISCRIMINANT VARIETIES - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2015

AUTOMORPHISM GROUPS OF CONFIGURATION SPACES AND DISCRIMINANT VARIETIES

Résumé

The configuration space $\mathcal{C}^n(X)$ of an algebraic curve $X$ is the algebraic variety consisting of all $n$-point subsets $Q\subset X$. We describe the automorphisms of $\mathcal{C}^n(\mathbb{C})$, deduce that the (infinite dimensional) group $\Aut\mathcal{C}^n(\mathbb{C})$ is solvable, and obtain an analog of the Mostow decomposition in this group. The Lie algebra and the Makar-Limanov invariant of $\mathcal{C}^n(\mathbb{C})$ are also computed. We obtain similar results for the level hypersurfaces of the discriminant, including its singular zero level. This is an extended version of our paper \cite{Lin-Zaidenberg14}. We strengthened the results concerning the automorphism groups of cylinders over rigid bases, replacing the rigidity assumption by the weaker assumption of tightness. We also added alternative proofs of two auxiliary results cited in \cite{Lin-Zaidenberg14} and due to Zinde and to the first author. This allowed us to provide the optimal dimension bounds in our theorems.
Fichier principal
Vignette du fichier
LZ_2015-preprint.pdf (675.77 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01150108 , version 1 (08-05-2015)

Identifiants

Citer

Vladimir Lin, Mikhail Zaidenberg. AUTOMORPHISM GROUPS OF CONFIGURATION SPACES AND DISCRIMINANT VARIETIES. 2015. ⟨hal-01150108⟩

Collections

CNRS FOURIER
197 Consultations
157 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More