Asymptotic behaviour of the sectional ring

Xiaojun Wu

doi:10.5802/crmath.651

Article de recherche - Analyse et géométrie complexes

Asymptotic behaviour of the sectional ring
[Comportement asymptotique de l’anneau canonique d’un fibré en droites]

Xiaojun Wu ¹

¹ Universität Bayreuth, Universitätsstraße 30, 95447 Bayreuth, Germany

Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1389-1397.

Résumé
Abstract

La théorie du corps d’Okounkov est un outil puissant pour analyser le comportement asymptotique de l’anneau canonique d’un fibré en droites sur une variété projective. Dans cette note, combiné avec la réduction algébrique, nous étudions le comportement asymptotique de l’anneau canonique d’un fibré en droites sur tout espace complexe compact, normal et irréductible arbitraire.

The theory of the Okounkov body is a usual tool for analyzing the asymptotic behaviour of the sectional ring of a line bundle over a projective manifold. In this note, combined with the algebraic reduction, we study the asymptotic behaviour of the sectional ring of a line bundle over any arbitrary compact, normal, irreducible complex space.

Reçu le : 2023-02-08
Révisé le : 2023-10-06
Accepté le : 2024-05-17
Publié le : 2024-11-14

DOI : 10.5802/crmath.651

Classification : 32C15, 32J18, 32S20
Keywords: Okounkov body, canonical ring, algebraic reduction
Mot clés : Corps d’Okounkov, anneau canonique, réduction algébrique

Affiliations des auteurs :

Xiaojun Wu ¹

¹ Universität Bayreuth, Universitätsstraße 30, 95447 Bayreuth, Germany

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Asymptotic behaviour of the sectional ring},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1389--1397},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {362},
     year = {2024},
     doi = {10.5802/crmath.651},
     language = {en},
}

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Xiaojun Wu. Asymptotic behaviour of the sectional ring. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1389-1397. doi : 10.5802/crmath.651. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.651/

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