On metrics with minimal singularities of line bundles whose stable base loci admit holomorphic tubular neighborhoods

Genki Hosono; Takayuki Koike

doi:10.5802/afst.1628

Genki Hosono ¹ ; Takayuki Koike ²

¹ Mathematical Institute, Tohoku University, 6-3, Aramaki Aza-Aoba, Aoba-ku, Sendai, 980-8578 (Japan)
² Graduate School of Science, Osaka City University, 3-3-138, Sugimoto, Sumiyoshi-ku Osaka, 558-8585 (Japan)

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 1, pp. 149-175.

Résumé
Abstract

Nous étudions les singularités minimales des métriques d’un fibre en droites $L$ sur une variété projective lorsque le locus de base stable $Y$ de $L$ est une sous-variété de codimension $r \geq 1$ . Sous certaines hypothèses sur le fibre normal et le voisinage de $Y$ , nous donnons une description explicite de la singularité minimale des métriques de $L$ . Nous appliquons ce résultat pour étudier un analogue (co-dimensionnel) plus élevé de l’exemple de Zariski, dans lequel le fibre en droites $L$ n’est pas semi-ample, mais il est nef et gros.

We investigate the minimal singularities of metrics on a big line bundle $L$ over a projective manifold when the stable base locus $Y$ of $L$ is a submanifold of codimension $r \geq 1$ . Under some assumptions on the normal bundle and a neighborhood of $Y$ , we give a explicit description of the minimal singularity of metrics on $L$ . We apply this result to study a higher (co-)dimensional analogue of Zariski’s example, in which the line bundle $L$ is not semi-ample, however it is nef and big.

Reçu le : 2017-07-25
Accepté le : 2018-01-29
Publié le : 2020-07-24

DOI : 10.5802/afst.1628

Affiliations des auteurs :

Genki Hosono ¹ ; Takayuki Koike ²

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Genki Hosono and Takayuki Koike},
     title = {On metrics with minimal singularities of line bundles whose stable base loci admit holomorphic tubular neighborhoods},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {149--175},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 29},
     number = {1},
     year = {2020},
     doi = {10.5802/afst.1628},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1628/}
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Genki Hosono; Takayuki Koike. On metrics with minimal singularities of line bundles whose stable base loci admit holomorphic tubular neighborhoods. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 1, pp. 149-175. doi : 10.5802/afst.1628. https://afst.centre-mersenne.org/articles/10.5802/afst.1628/

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