VANISHING COHOMOLOGY FOR HOLOMORPHIC VECTOR BUNDLES IN A BANACH SETTING

Stable holomorphic vector bundles over complex projective space ℙnhave been studied from both the differential-geometric and the algebraic-geometric points of view.On the differential-geometric side, the stability ofE-→ ℙncan be characterized by the existence of a unique hermitian–Einstein metric onE, i.e. a metric whose curvature matrix has trace-free part orthogonal to the Fubini–Study Kähler form of ℙn(see [6], [7], and [13]). Very little is known about this metric in general and the only explicit examples are the metrics on the tangent bundle of ℙnand the nullcorrelation bundle (see [9] and [10]).

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Union of linear spaces in infinite-dimensional projective spaces and holomorphic vector bundles

Results in Mathematics ◽

10.1007/bf03322737 ◽

2003 ◽

Vol 43 (3-4) ◽

pp. 202-204

Author(s):

E. Ballico

Keyword(s):

Vector Bundles ◽

Projective Spaces ◽

Linear Spaces ◽

Infinite Dimensional ◽

Holomorphic Vector Bundles

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Holomorphic Vector Bundles and the Geometry of ℙn

Vector Bundles on Complex Projective Spaces - Progress in Mathematics ◽

10.1007/978-1-4757-1460-9_1 ◽

1980 ◽

pp. 1-138

Author(s):

Christian Okonek ◽

Michael Schneider ◽

Heinz Spindler

Keyword(s):

Vector Bundles ◽

Holomorphic Vector Bundles

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Complex Finsler structures on tensor products

Advances in Geometry ◽

10.1515/advgeom-2015-0038 ◽

2016 ◽

Vol 16 (1) ◽

Author(s):

Adnène Ben Abdesselem ◽

Ines Adouan

Keyword(s):

Vector Bundles ◽

Tensor Products ◽

Holomorphic Vector Bundles

AbstractGiven two holomorphic vector bundles E

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Holomorphic Vector Bundles on Holomorphically Convex Complex Manifolds

Georgian Mathematical Journal ◽

10.1515/gmj.2006.7 ◽

2006 ◽

Vol 13 (1) ◽

pp. 7-10

Author(s):

Edoardo Ballico

Keyword(s):

Vector Bundle ◽

Complex Manifold ◽

Vector Bundles ◽

Open Neighborhood ◽

Holomorphic Vector Bundle ◽

Stein Manifold ◽

Complex Manifolds ◽

Holomorphic Vector Bundles

Abstract Let 𝑋 be a holomorphically convex complex manifold and Exc(𝑋) ⊆ 𝑋 the union of all positive dimensional compact analytic subsets of 𝑋. We assume that Exc(𝑋) ≠ 𝑋 and 𝑋 is not a Stein manifold. Here we prove the existence of a holomorphic vector bundle 𝐸 on 𝑋 such that is not holomorphically trivial for every open neighborhood 𝑈 of Exc(𝑋) and every integer 𝑚 ≥ 0. Furthermore, we study the existence of holomorphic vector bundles on such a neighborhood 𝑈, which are not extendable across a 2-concave point of ∂(𝑈).

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