We investigate Hermitian metrics on the anti-canonical bundle of a rational surface obtained by blowing up the projective plane at nine points. For that purpose, we pose a modified variant of an argument made by Ueda on the complex analytic structure of a neighborhood of a subvariety by considering the deformation of the complex structure.
Nous étudions les métriques hermitiennes sur le faisceau anticanonique d’une surface rationnelle obtenue en éclatant le plan projectif en neuf points. Dans ce but nous utilisons une variante modifiée d’un argument de Ueda sur la structure analytique complexe d’un voisinage d’une sous-variété en considérant la déformation de la structure complexe.
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Keywords: The blow-up of the projective plane at nine points, Hermitian metrics, neighborhoods of subvarieties, Ueda theory
Koike, Takayuki 1
CC-BY 4.0
@article{AFST_2023_6_32_2_231_0,
author = {Koike, Takayuki},
title = {Hermitian metrics on the anti-canonical bundle of the blow-up of the projective plane at nine points},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {231--285},
year = {2023},
publisher = {Universit\'e Paul Sabatier, Toulouse},
volume = {Ser. 6, 32},
number = {2},
doi = {10.5802/afst.1736},
language = {en},
url = {https://www.numdam.org/articles/10.5802/afst.1736/}
}
TY - JOUR AU - Koike, Takayuki TI - Hermitian metrics on the anti-canonical bundle of the blow-up of the projective plane at nine points JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2023 SP - 231 EP - 285 VL - 32 IS - 2 PB - Université Paul Sabatier, Toulouse UR - https://www.numdam.org/articles/10.5802/afst.1736/ DO - 10.5802/afst.1736 LA - en ID - AFST_2023_6_32_2_231_0 ER -
%0 Journal Article %A Koike, Takayuki %T Hermitian metrics on the anti-canonical bundle of the blow-up of the projective plane at nine points %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2023 %P 231-285 %V 32 %N 2 %I Université Paul Sabatier, Toulouse %U https://www.numdam.org/articles/10.5802/afst.1736/ %R 10.5802/afst.1736 %G en %F AFST_2023_6_32_2_231_0
Koike, Takayuki. Hermitian metrics on the anti-canonical bundle of the blow-up of the projective plane at nine points. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 32 (2023) no. 2, pp. 231-285. doi: 10.5802/afst.1736
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