A non-vanishing conjecture for cotangent bundles on elliptic surfaces

Haesong Seo

doi:10.5802/crmath.721

Article de recherche - Géométrie algébrique

A non-vanishing conjecture for cotangent bundles on elliptic surfaces
[Une conjecture de non-annulation pour les fibrés cotangents sur les surfaces elliptiques]

Haesong Seo ¹

¹ Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Deajeon, 34141, Republic of Korea

Comptes Rendus. Mathématique, Volume 363 (2025), pp. 487-497.

Abstract (VO)
Résumé

In this paper, we prove the non-vanishing conjecture for cotangent bundles on isotrivial elliptic surfaces. Combined with the result by Höring and Peternell, it completely solves the question for surfaces with Kodaira dimension at most $1$ .

Dans cet article, nous prouvons la conjecture de non-annulation pour les fibrés cotangents sur les surfaces elliptiques isotriviales. Combiné avec le résultat de Höring et Peternell, cela résout complètement la question pour les surfaces de dimension de Kodaira au plus $1$ .

Reçu le : 2024-07-02
Révisé le : 2024-12-07
Accepté le : 2025-01-23
Publié le : 2025-05-26

DOI : 10.5802/crmath.721

Classification : 14E05, 14J27
Keywords: Non-vanishing conjecture, symmetric differential, elliptic surface
Mots-clés : Conjecture de non-annulation, différentielle symétrique, surface elliptique

Affiliations des auteurs :

Haesong Seo ¹

¹ Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Deajeon, 34141, Republic of Korea

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {A non-vanishing conjecture for cotangent bundles on elliptic surfaces},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {487--497},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {363},
     year = {2025},
     doi = {10.5802/crmath.721},
     language = {en},
}

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Haesong Seo. A non-vanishing conjecture for cotangent bundles on elliptic surfaces. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 487-497. doi : 10.5802/crmath.721. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.721/

Bibliographie
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