Lefschetz section theorems for tropical hypersurfaces

Arnal, Charles; Renaudineau, Arthur; Shaw, Kris

Document type :

Article dans une revue scientifique: Article original

DOI :

10.5802/ahl.104

Title :

Lefschetz section theorems for tropical hypersurfaces

Author(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]

Journal title :

Annales Henri Lebesgue

Pages :

1347-1387

Publisher :

UFR de Mathématiques - IRMAR

Publication date :

2021-09-22

ISSN :

2644-9463

HAL domain(s) :

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

English abstract : [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 ...
Show more >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.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

Collections :