The geometry of the Coble cubic and orbital degeneracy loci

Benedetti, Vladimiro; Manivel, Laurent; Tanturri, Fabio

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1007/s00208-019-01949-7

Title :

The geometry of the Coble cubic and orbital degeneracy loci

Author(s) :

Benedetti, Vladimiro [Auteur]
Département de Mathématiques et Applications - ENS Paris [DMA]
Manivel, Laurent [Auteur]
Institut de Mathématiques de Toulouse UMR5219 [IMT]
Tanturri, Fabio [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Mathematische Annalen

Pages :

415-440

Publisher :

Springer Verlag

Publication date :

2021-02

ISSN :

0025-5831

HAL domain(s) :

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

English abstract : [en]

The Coble cubics were discovered more than a century ago in connection with genus two Riemann surfaces and theta functions. They have attracted renewed interest ever since. Recently, they were reinterpreted in terms of ...
Show more >The Coble cubics were discovered more than a century ago in connection with genus two Riemann surfaces and theta functions. They have attracted renewed interest ever since. Recently, they were reinterpreted in terms of alternating trivectors in nine variables. Exploring this relation further, we show how the Hilbert scheme of pairs of points on an abelian surface, and also its Kummer fourfold, a very remarkable hyper-Kähler manifold, can very naturally be constructed in this context. Moreover, we explain how this perspective allows us to describe the group law of an abelian surface, in a strikingly similar way to how the group structure of a plane cubic can be defined in terms of its intersection with lines.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :