UNIFORMITY OF HOLOMORPHIC VECTOR BUNDLES ON INFINITE-DIMENSIONAL FLAG MANIFOLDS

Title & Authors
UNIFORMITY OF HOLOMORPHIC VECTOR BUNDLES ON INFINITE-DIMENSIONAL FLAG MANIFOLDS
Ballico, E.;

Abstract
Let V be a localizing infinite-dimensional complex Banach space. Let X be a flag manifold of finite flags either of finite codimensional closed linear subspaces of V or of finite dimensional linear subspaces of V. Let E be a holomorphic vector bundle on X with finite rank. Here we prove that E is uniform, i.e. that for any two lines $\small{D_1}$ R in the same system of lines on X the vector bundles E$\small{\mid}$D and E$\small{\mid}$R have the same splitting type.
Keywords
flag manifold;infinite-dimensional flag manifold;holo-morphic vector bundle;uniform vector bundle;splitting type;
Language
English
Cited by
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