Title :

ACTION OF THE AUTOMORPHISM GROUP ON THE JACOBIAN OF KLEIN'S QUARTIC CURVE II: INVARIANT THETA-FUNCTIONS

Author(s) :

Markushevich, Dimitri [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Moreau, Anne [Auteur]
Laboratoire de Mathématiques d'Orsay [LMO]

Journal title :

Épijournal de Géométrie Algébrique

Publisher :

EPIGA

Publication date :

2024

ISSN :

2491-6765

HAL domain(s) :

Mathématiques [math]/Géométrie algébrique [math.AG]

English abstract : [en]

Bernstein-Schwarzman conjectured that the quotient of a complex affine space by an irreducible complex crystallographic group generated by reflections is a weighted projective space. The conjecture was proved by Schwarzman ...
Show more >Bernstein-Schwarzman conjectured that the quotient of a complex affine space by an irreducible complex crystallographic group generated by reflections is a weighted projective space. The conjecture was proved by Schwarzman and Tokunaga-Yoshida in dimension 2 for almost all such groups, and for all crystallographic reflection groups of Coxeter type by Looijenga, Bernstein-Schwarzman and Kac-Peterson in any dimension. We prove that the conjecture is true for the crystallographic reflection group in dimension 3 for which the associated collineation group is Klein's simple group of order 168. In this case the quotient is the 3-dimensional weighted projective space with weights 1, 2, 4, 7. The main ingredient in the proof is the computation of the algebra of invariant theta-functions. Unlike the Coxeter case, the invariant algebra is not free polynomial, and this was the major stumbling block.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions
Symétries et espaces de modules en géométrie algébrique et physique

Comment :

23 pages, 1 figure. Introduction and abstract rewritten, references updated

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL