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On metrics with minimal singularities of line bundles whose stable base loci admit holomorphic tubular neighborhoods
Genki Hosono1; Takayuki Koike2
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, Serie 6, Volume 29 (2020) no. 1, pp. 149-175.

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≥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.

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≥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.

Received:
Accepted:
Published online:
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)
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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     title = {On metrics with minimal singularities of line bundles whose stable base loci admit holomorphic tubular neighborhoods},
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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, Serie 6, Volume 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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