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Projective Bundles on Infinite-Dimensional Complex Spaces
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E. Ballico
Veröffentlicht/Copyright:
3. März 2010
Abstract
Let V be a complex localizing Banach space with countable unconditional basis and E a rank r holomorphic vector bundle on P(V). Here we study the holomorphic embeddings of P(E) into products of projective spaces and the holomorphic line bundles on P(E). In particular we prove that if r ≥ 3, then H1(P(E), L) = 0 for every holomorphic line bundle L on P(E).
Key words and phrases:: Infinite-dimensional projective space; complex Banach manifold; holomorphic vector bundle; holomorphic line bundle; localizing Banach space; Banach space with countable unconditional basis
Received: 2003-04-24
Revised: 2003-10-17
Published Online: 2010-03-03
Published in Print: 2004-March
© Heldermann Verlag
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Artikel in diesem Heft
- Some Integral Operators which Preserve a Subclass of Uniformly Quasiconvex Functions
- Linearization and Higher Order Nonlinear Oscillation Theorems Using Comparison Methods
- The Structure of 𝐺-Free Nilpotent Groups of Step 3
- Fuzzy Solutions for Neutral Functional Differential Equations with Nonlocal Conditions
- Projective Bundles on Infinite-Dimensional Complex Spaces
- Explicit Solutions of the Basic Boundary Value Problems of Statics of the Elastic Mixture Theory for an Annulus
- Particular Solutions for a Class of ODE Related to the L-Exponential Functions
- On Hyers–Ulam Stability of Cauchy and Wilson Equations
- Common Fixed Points Iteration Processes for a Finite Family of Asymptotically Nonexpansive Mappings
- Varieties of Universal Algebras with Normal Local Projections
- Integrability and L1-Convergence of Modified Sine Sums
- On Homogeneous Coverings of Euclidean Spaces
- On Entire Modular Forms of Half-Integral Weight on the Congruence Subgroup Γ0(4N)
- The Bellman Equation Related to the Minimal Entropy Martingale Measure
- Oscillation and Nonoscillation Criteria for two-Dimensional Systems of Linear Ordinary Differential Equations
- Formulas of Variation for a Solution of Neutral Differential Equations with Continuous Initial Condition
- Positive Solutions of a Neutral Difference Equation with Positive and Negative Coefficients
- Two Sharp Inequalities of Simpson Type and Applications
- On the Equivalence between Ch and The Existence of Certain I-Luzin Subsets of ℝ
