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.
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.
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@article{AFST_2023_6_32_2_231_0,
author = {Takayuki Koike},
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},
publisher = {Universit\'e Paul Sabatier, Toulouse},
volume = {Ser. 6, 32},
number = {2},
year = {2023},
doi = {10.5802/afst.1736},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1736/}
}
TY - JOUR AU - Takayuki Koike 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://afst.centre-mersenne.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 Takayuki Koike %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://afst.centre-mersenne.org/articles/10.5802/afst.1736/ %R 10.5802/afst.1736 %G en %F AFST_2023_6_32_2_231_0
Takayuki Koike. 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. https://afst.centre-mersenne.org/articles/10.5802/afst.1736/
[1] Bifurcations of invariant manifolds of differential equations and normal forms in neighborhoods of elliptic curves, Funkts. Anal. Prilozh., Volume 10 (1976) no. 4, pp. 1-12 | Zbl
[2] On Kähler surfaces with semipositive Ricci curvature, Riv. Mat. Univ. Parma, Volume 1 (2010) no. 2, pp. 441-450 | Zbl
[3] Compact leaves of codimension one holomorphic foliations on projective manifolds, Ann. Sci. Éc. Norm. Supér., Volume 51 (2018) no. 6, pp. 1457-1506 | DOI | MR | Zbl
[4] Complex analytic and differential geometry (https://www-fourier.ujf-grenoble.fr/~demailly/manuscripts/agbook.pdf)
[5] Structure Theorems for Compact Kähler Manifolds with Nef Anticanonical Bundles, Complex analysis and geometry. KSCV 10 (Springer Proceedings in Mathematics & Statistics), Volume 144, Springer, 2015, pp. 119-133 | DOI | Zbl
[6] Compact complex manifolds with numerically effective tangent bundles, J. Algebr. Geom., Volume 3 (1994) no. 2, pp. 295-345 | MR | Zbl
[7] Classification theories of polarized varieties, London Mathematical Society Lecture Note Series, 155, London Mathematical Society, 1990 | DOI
[8] A theorem of completeness of characteristic systems of complete continuous systems, Am. J. Math., Volume 81 (1959), pp. 477-500 | DOI | MR
[9] On minimal singular metrics of certain class of line bundles whose section ring is not finitely generated, Ann. Inst. Fourier, Volume 65 (2015) no. 5, pp. 1953-1967 | DOI | Numdam | MR | Zbl
[10] On the minimality of canonically attached singular Hermitian metrics on certain nef line bundles, Kyoto J. Math., Volume 55 (2015) no. 3, pp. 607-616 | MR | Zbl
[11] Toward a higher codimensional Ueda theory, Math. Z., Volume 281 (2015) no. 3-4, pp. 967-991 | DOI | MR | Zbl
[12] Ueda theory for compact curves with nodes, Indiana Univ. Math. J., Volume 66 (2017) no. 3, pp. 845-876 | DOI | MR | Zbl
[13] Higher codimensional Ueda theory for a compact submanifold with unitary flat normal bundle, Nagoya Math. J., Volume 238 (2018), pp. 104-136 | DOI | MR | Zbl
[14] Plurisubharmonic functions on a neighborhood of a torus leaf of a certain class of foliations, Forum Math., Volume 31 (2019) no. 6, pp. 1457-1466 | DOI | MR
[15] Local criteria for non embeddability of Levi-flat manifolds, J. Geom. Anal., Volume 28 (2018) no. 2, pp. 1052-1077 | DOI | MR | Zbl
[16] On the neighborhood of a torus leaf and dynamics of holomorphic foliations (2018) (https://arxiv.org/abs/1808.10219)
[17] A gluing construction of K3 surfaces (2019) (https://arxiv.org/abs/1903.01444)
[18] Ueda theory: theorems and problems, Memoirs of the American Mathematical Society, American Mathematical Society, 1989 no. 415, 123 pages
[19] Iterations of analytic functions, Ann. Math., Volume 43 (1942), pp. 607-612 | DOI | MR
[20] Every Stein subvariety admits a Stein neighborhood, Invent. Math., Volume 38 (1976), pp. 89-100 | MR | Zbl
[21] On the neighborhood of a compact complex curve with topologically trivial normal bundle, J. Math. Kyoto Univ., Volume 22 (1983), pp. 583-607 | MR
[22] Neighborhood of a rational curve with a node, Publ. Res. Inst. Math. Sci., Volume 27 (1991) no. 4, pp. 681-693 | DOI | MR | Zbl
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