Corrigendum to: Holomorphic Morse inequalities on manifolds with boundary

Robert Berman

Displaying similar documents to “Corrigendum to: Holomorphic Morse inequalities on manifolds with boundary”

Holomorphic Morse Inequalities on Manifolds with Boundary

Robert Berman (2005)

Annales de l’institut Fourier

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Let $X$ be a compact complex manifold with boundary and let $L^{k}$ be a high power of a hermitian holomorphic line bundle over $X .$ When $X$ has no boundary, Demailly’s holomorphic Morse inequalities give asymptotic bounds on the dimensions of the Dolbeault cohomology groups with values in $L^{k},$ in terms of the curvature of $L .$ We extend Demailly’s inequalities to the case when $X$ has a boundary by adding a boundary term expressed as a certain average of the curvature of the line bundle and the Levi curvature of...

A survey of boundary value problems for bundles over complex spaces

Harris, Adam

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Let $X$ be a reduced $n$ -dimensional complex space, for which the set of singularities consists of finitely many points. If $X^{'} \subseteq X$ denotes the set of smooth points, the author considers a holomorphic vector bundle $E \to X^{'} ∖ A$ , equipped with a Hermitian metric $h$ , where $A$ represents a closed analytic subset of complex codimension at least two. The results, surveyed in this paper, provide criteria for holomorphic extension of $E$ across $A$ , or across the singular points of $X$ if $A = ⌀$ . The approach taken here is...

An effective Matsusaka big theorem

Yum-Tong Siu (1993)

Annales de l'institut Fourier

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Analytic cohomology of complete intersections in a Banach space

Imre Patyi (2004)

Annales de l’institut Fourier

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Let $X$ be a Banach space with a countable unconditional basis (e.g., $X = ℓ_{2}$ ), $Ω \subset X$ an open set and $f_{1}, ..., f_{k}$ complex-valued holomorphic functions on $Ω$ , such that the Fréchet differentials $d f_{1} (x), ..., d f_{k} (x)$ are linearly independant over $ℂ$ at each $x \in Ω$ . We suppose that $M = {x \in Ω : f_{1} (x) = ... = f_{k} (x) = 0}$ is a complete intersection and we consider a holomorphic Banach vector bundle $E \to M$ . If $I$ (resp. $𝒪^{E}$ ) denote the ideal of germs of holomorphic functions on $Ω$ that vanish on $M$ (resp. the sheaf of germs of holomorphic sections of $E$ ), then the sheaf cohomology groups...