Nous étudions les singularités minimales des métriques d’un fibre en droites sur une variété projective lorsque le locus de base stable de est une sous-variété de codimension . Sous certaines hypothèses sur le fibre normal et le voisinage de , nous donnons une description explicite de la singularité minimale des métriques de . Nous appliquons ce résultat pour étudier un analogue (co-dimensionnel) plus élevé de l’exemple de Zariski, dans lequel le fibre en droites n’est pas semi-ample, mais il est nef et gros.
We investigate the minimal singularities of metrics on a big line bundle over a projective manifold when the stable base locus of is a submanifold of codimension . Under some assumptions on the normal bundle and a neighborhood of , we give a explicit description of the minimal singularity of metrics on . We apply this result to study a higher (co-)dimensional analogue of Zariski’s example, in which the line bundle is not semi-ample, however it is nef and big.
Accepté le :
Publié le :
Genki Hosono 1 ; Takayuki Koike 2

@article{AFST_2020_6_29_1_149_0, 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/} }
TY - JOUR AU - Genki Hosono AU - Takayuki Koike TI - On metrics with minimal singularities of line bundles whose stable base loci admit holomorphic tubular neighborhoods JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2020 SP - 149 EP - 175 VL - 29 IS - 1 PB - Université Paul Sabatier, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1628/ DO - 10.5802/afst.1628 LA - en ID - AFST_2020_6_29_1_149_0 ER -
%0 Journal Article %A Genki Hosono %A Takayuki Koike %T On metrics with minimal singularities of line bundles whose stable base loci admit holomorphic tubular neighborhoods %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2020 %P 149-175 %V 29 %N 1 %I Université Paul Sabatier, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1628/ %R 10.5802/afst.1628 %G en %F AFST_2020_6_29_1_149_0
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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