Lefschetz section theorems for tropical hypersurfaces

Arnal, Charles; Renaudineau, Arthur; Shaw, Kris

Type de document :

Article dans une revue scientifique: Article original

DOI :

10.5802/ahl.104

Titre :

Lefschetz section theorems for tropical hypersurfaces

Auteur(s) :

Arnal, Charles [Auteur]
Understanding the Shape of Data [DATASHAPE]
Renaudineau, Arthur [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]
Shaw, Kris [Auteur]
University of Oslo [UiO]

Titre de la revue :

Annales Henri Lebesgue

Pagination :

1347-1387

Éditeur :

UFR de Mathématiques - IRMAR

Date de publication :

2021-09-22

ISSN :

2644-9463

Discipline(s) HAL :

Mathématiques [math]/Mathématiques générales [math.GM]

Résumé en anglais : [en]

We establish variants of the Lefschetz section theorem for the integral tropical homology groups of tropical hypersurfaces of tropical toric varieties. It follows from these theorems that the integral tropical homology ...
Lire la suite >We establish variants of the Lefschetz section theorem for the integral tropical homology groups of tropical hypersurfaces of tropical toric varieties. It follows from these theorems that the integral tropical homology groups of non-singular tropical hypersurfaces which are compact or contained in Rn are torsion free. We prove a relationship between the coefficients of the χy genera of complex hypersurfaces in toric varieties and Euler characteristics of the integral tropical cellular chain complexes of their tropical counterparts. It follows that the integral tropical homology groups give the Hodge numbers of compact non-singular hypersurfaces of complex toric varieties. Finally for tropical hypersurfaces in certain affine toric varieties, we relate the ranks of their tropical homology groups to the Hodge–Deligne numbers of their complex counterparts.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Projet ANR :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :