The Atiyah class of generalized holomorphic vector bundles

被引：0

作者：

Lang, Honglei ^{[1
]}

Jia, Xiao ^{[2
]}

Liu, Zhangju ^{[3
]}

机构：

[1] China Agr Univ, Coll Sci, Beijing 100873, Peoples R China

[2] Peking Univ, Sch Math, Beijing 100871, Peoples R China

[3] Henan Univ, Sch Math & Stat Sci, Kaifeng 475004, Peoples R China

来源：

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2023年 / 90卷

关键词：

Atiyah class; Generalized complex structure;

D O I：

10.1016/j.difgeo.2023.102031

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce the notion of Atiyah class of a generalized holomorphic vector bundle, which captures the obstruction to the existence of generalized holomorphic connections on the bundle. As in the classical holomorphic case, this Atiyah class can be defined in three different ways: using Cech cohomology, using the first-jet short exact sequence, or adopting the Lie pair point of view.& COPY; 2023 Elsevier B.V. All rights reserved.

引用

页数：25

共 50 条

[41] On holomorphic Banach vector bundles over Banach spaces
Patyi, Imre
MATHEMATISCHE ANNALEN, 2008, 341 (02) : 455 - 482
[42] Nonorientable Manifolds, Complex Structures, and Holomorphic Vector Bundles
Indranil Biswas
Avijit Mukherjee
Acta Applicandae Mathematica, 2001, 69 : 25 - 42
[43] HOLOMORPHIC TENSORS AND VECTOR-BUNDLES ON PROJECTIVE VARIETIES
BOGOMOLOV, FA
MATHEMATICS OF THE USSR-IZVESTIYA, 1979, 13 (03): : 499 - 555
[44] Holomorphic vector bundles on C2\{0}
Ballico, E
ISRAEL JOURNAL OF MATHEMATICS, 2002, 128 (1) : 197 - 204
[45] CURVATURE AND LINEAR SUBBUNDLES OF HOLOMORPHIC VECTOR-BUNDLES
CHINAK, MA
FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 1989, 23 (02) : 164 - 165
[46] Holomorphic vector bundles on open subsets of Stein manifolds
Ballico, E
ISRAEL JOURNAL OF MATHEMATICS, 2003, 133 (1) : 89 - 91
[47] ON PROJECTIVIZED VECTOR BUNDLES AND POSITIVE HOLOMORPHIC SECTIONAL CURVATURE
Alvarez, Angelynn
Heier, Gordon
Zheng, Fangyang
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2018, 146 (07) : 2877 - 2882
[48] Holomorphic vector bundles on non-algebraic surfaces
Teleman, A
Toma, M
COMPTES RENDUS MATHEMATIQUE, 2002, 334 (05) : 383 - 388
[49] Holomorphic vector bundles on open subsets of Stein manifolds
E. Ballico
Israel Journal of Mathematics, 2003, 133 : 89 - 91
[50] DEFORMATIONS OF COMPLEX STRUCTURES AND HOLOMORPHIC VECTOR-BUNDLES
NARASIMHAN, MS
LECTURE NOTES IN MATHEMATICS, 1982, 950 : 196 - 209

← 1 2 3 4 5 →