Existence of Good Minimal Models for Kähler varieties of Maximal Albanese Dimension

Omprokash Das; Christopher Hacon

doi:10.5802/crmath.581

Article de recherche - Géométrie algébrique

Existence of Good Minimal Models for Kähler varieties of Maximal Albanese Dimension
[Existence d’un bon modèle minimal pour les variétés kählériennes de dimension d’Albanese maximale]

Omprokash Das ¹ ; Christopher Hacon ²

¹ School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Navy Nagar, Colaba, Mumbai 400005
² Department of Mathematics, University of Utah, 155 S 1400 E, Salt Lake City, Utah 84112, USA

Comptes Rendus. Mathématique, Volume 362 (2024) no. S1, pp. 83-91.

Résumé
Abstract

Dans ce court article, nous montrons que si $(X, B)$ est une paire kählérienne compacte klt de dimension d’Albanese maximale, $(X, B)$ admet un bon modèle minimal, c’est-à-dire qu’il existe une contraction biméromorphe $ϕ : X ⤏ X^{'}$ telle que $K_{X^{'}} + B^{'}$ est semi-ample.

In this short article we show that if $(X, B)$ is a compact Kähler klt pair of maximal Albanese dimension, then it has a good minimal model, i.e. there is a bimeromorphic contraction $ϕ : X ⤏ X^{'}$ such that $K_{X^{'}} + B^{'}$ is semi-ample.

Reçu le : 2022-12-06
Accepté le : 2023-07-18
Publié le : 2024-06-06

DOI : 10.5802/crmath.581

Affiliations des auteurs :

Omprokash Das ¹ ; Christopher Hacon ²

¹ School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Navy Nagar, Colaba, Mumbai 400005
² Department of Mathematics, University of Utah, 155 S 1400 E, Salt Lake City, Utah 84112, USA

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Omprokash Das and Christopher Hacon},
     title = {Existence of {Good} {Minimal} {Models} for {K\"ahler} varieties of {Maximal} {Albanese} {Dimension}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {83--91},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {362},
     number = {S1},
     year = {2024},
     doi = {10.5802/crmath.581},
     language = {en},
}

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Omprokash Das; Christopher Hacon. Existence of Good Minimal Models for Kähler varieties of Maximal Albanese Dimension. Comptes Rendus. Mathématique, Volume 362 (2024) no. S1, pp. 83-91. doi : 10.5802/crmath.581. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.581/

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