Displaying similar documents to “Holomorphic vector bundles on certain holomorphically convex complex manifolds”

Natural operations on holomorphic forms

A. Navarro, J. Navarro, C. Tejero Prieto (2018)

Archivum Mathematicum

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We prove that the only natural differential operations between holomorphic forms on a complex manifold are those obtained using linear combinations, the exterior product and the exterior differential. In order to accomplish this task we first develop the basics of the theory of natural holomorphic bundles over a fixed manifold, making explicit its Galoisian structure by proving a categorical equivalence à la Galois.

Extending holomorphic mappings from subvarieties in Stein manifolds

Franc Forstneric (2005)

Annales de l’institut Fourier

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Suppose that Y is a complex manifold such that any holomorphic map from a compact convex set in a Euclidean space n to Y is a uniform limit of entire maps n Y . We prove that a holomorphic map X 0 Y from a closed complex subvariety X 0 in a Stein manifold X admits a holomorphic extension X Y provided that it admits a continuous extension. We then establish the equivalence of four Oka-type properties of a complex manifold.

Vector bundles over Dold manifolds

R. E. Stong (2001)

Fundamenta Mathematicae

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This paper determines the possible Stiefel-Whitney classes for vector bundles over Dold manifolds.

Holomorphic submersions from Stein manifolds

Franc Forstnerič (2004)

Annales de l’institut Fourier

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We establish the homotopy classification of holomorphic submersions from Stein manifolds to Complex manifolds satisfying an analytic property introduced in the paper. The result is a holomorphic analogue of the Gromov--Phillips theorem on smooth submersions.