Page 1 Next

## Displaying 1 – 20 of 82

Showing per page

### A cohomological Steinness criterion for holomorphically spreadable complex spaces

Czechoslovak Mathematical Journal

Let $X$ be a complex space of dimension $n$, not necessarily reduced, whose cohomology groups ${H}^{1}\left(X,𝒪\right),...,{H}^{n-1}\left(X,𝒪\right)$ are of finite dimension (as complex vector spaces). We show that $X$ is Stein (resp., $1$-convex) if, and only if, $X$ is holomorphically spreadable (resp., $X$ is holomorphically spreadable at infinity). This, on the one hand, generalizes a known characterization of Stein spaces due to Siu, Laufer, and Simha and, on the other hand, it provides a new criterion for $1$-convexity.

### A Differential Geometrie Criterion for Moishezon Spaces.

Mathematische Annalen

### A finiteness theorem for holomorphic Banach bundles

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let $E$ be a holomorphic Banach bundle over a compact complex manifold, which can be defined by a cocycle of holomorphic transition functions with values of the form $\mathrm{id}+K$ where $K$ is compact. Assume that the characteristic fiber of $E$ has the compact approximation property. Let $n$ be the complex dimension of $X$ and $0\le q\le n$. Then: If $V\to X$ is a holomorphic vector bundle (of finite rank) with ${H}^{q}\left(X,V\right)=0$, then $dim{H}^{q}\left(X,V\otimes E\right)<\infty$. In particular, if $dim{H}^{q}\left(X,𝒪\right)=0$, then $dim{H}^{q}\left(X,E\right)<\infty$.

### A Generalization of Kodaira-Ramanujam's Vanishing Theorem.

Mathematische Annalen

### A Geometry of Kähler Cones.

Mathematische Annalen

### A remark on a non-vanishing theorem of P. Deligne and G. D. Mostow.

Journal für die reine und angewandte Mathematik

### A Topological Criterion for Local Optimality of Weakly Normal Complex Spaces.

Mathematische Annalen

### A vanishing theorem for Dolbeault cohomology of homogeneous vector bundles.

Journal für die reine und angewandte Mathematik

### A vanishing theorem on arithmetic surfaces.

Inventiones mathematicae

### Analytic cohomology of complete intersections in a Banach space

Annales de l’institut Fourier

Let $X$ be a Banach space with a countable unconditional basis (e.g., $X={\ell }_{2}$), $\Omega \subset X$ an open set and ${f}_{1},...,{f}_{k}$ complex-valued holomorphic functions on $\Omega$, such that the Fréchet differentials $d{f}_{1}\left(x\right),...,d{f}_{k}\left(x\right)$ are linearly independant over $ℂ$ at each $x\in \Omega$. We suppose that $M=\left\{x\in \Omega :{f}_{1}\left(x\right)=...={f}_{k}\left(x\right)=0\right\}$ 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 $\Omega$ that vanish on $M$ (resp. the sheaf of germs of holomorphic sections of $E$), then the sheaf cohomology groups ${H}^{q}\left(\Omega ,I\right)$, ${H}^{q}\left(M,{𝒪}^{E}\right)$ vanish...

### Annulation de la cohomologie à valeurs dans le faisceau structural et espaces de Stein

Compositio Mathematica

### Approximation and cohomology vanishing properties of low-dimensional compact sets in a Stein manifold.

Mathematische Zeitschrift

### Branched coverings and minimal free resolution for infinite-dimensional complex spaces.

Georgian Mathematical Journal

### Cohomologically complete and pseudoconvex domains.

Commentarii mathematici Helvetici

### Cohomology and splitting of Hermitian-Einstein vector bundles.

Mathematische Annalen

### Cohomology groups of sheaves SεL and splitness of Dolbeault complexes of sheaves ${J}_{V,\xi }$

Studia Mathematica

### Cohomology of Twisted Holomorphic Forms on Grassmann Manifolds and Quadric Hypersurfaces.

Mathematische Annalen

### Complex Analytic Cones.

Mathematische Annalen

### Corrigendum to: Holomorphic Morse inequalities on manifolds with boundary

Annales de l’institut Fourier

A statement in the paper “Holomorphic Morse inequalities on manifolds with boundary” saying that the holomorphic Morse inequalities for an hermitian line bundle $L$ over $X$ are sharp as long as $L$ extends as semi-positive bundle over a Stein-filling is corrected, by adding certain assumptions. A more general situation is also treated.

### Cyclic Coverings: Deformation and Torelli Theorem.

Mathematische Annalen

Page 1 Next