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Nakano–Nadel type, Bogomolov–Sommese type vanishing and singular dual Nakano semi-positivity
Yuta Watanabe1
1 Department of Mathematics, Faculty of Science and Engineering, Chuo University. 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 34 (2025) no. 2, pp. 339-394

In this article, we get properties for singular (dual) Nakano semi-positivity and obtain vanishing theorems involving $L^2$-subsheaves on weakly pseudoconvex manifolds by $L^2$-estimates and $L^2$-type Dolbeault isomorphisms. As applications, Fujita’s conjecture type theorem with singular Hermitian metrics is presented.

Dans cet article, nous obtenons des propriétés de semi-positivité singulière (duale) de Nakano et obtenons des théorèmes de disparition impliquant des sous-faisceaux $L^2$ sur des variétés faiblement pseudoconvexes par des estimations $L^2$ et des isomorphismes de Dolbeault de type $L^2$. En tant qu’applications, un théorème de type conjecture de Fujita avec des métriques hermitiennes singulières est présenté.

Received:
Accepted:
Published online:
DOI: 10.5802/afst.1815
Classification: 14F17, 14F18, 32L10, 32L20
Keywords: $L^2$-estimates, singular Hermitian metrics, cohomology vanishing

Yuta Watanabe 1

1 Department of Mathematics, Faculty of Science and Engineering, Chuo University. 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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     title = {Nakano{\textendash}Nadel type, {Bogomolov{\textendash}Sommese} type vanishing and singular dual {Nakano} semi-positivity},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
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Yuta Watanabe. Nakano–Nadel type, Bogomolov–Sommese type vanishing and singular dual Nakano semi-positivity. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 34 (2025) no. 2, pp. 339-394. doi: 10.5802/afst.1815

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