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Projective Bundles on Infinite-Dimensional Complex Spaces

Projective Bundles on Infinite-Dimensional Complex Spaces 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 H 1 ( P ( E ), L ) = 0 for every holomorphic line bundle L on P ( E ). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

Projective Bundles on Infinite-Dimensional Complex Spaces

Georgian Mathematical Journal , Volume 11 (1) – Mar 1, 2004

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References (14)

Publisher
de Gruyter
Copyright
© Heldermann Verlag
ISSN
1072-947X
eISSN
1072-9176
DOI
10.1515/GMJ.2004.43
Publisher site
See Article on Publisher Site

Abstract

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 H 1 ( P ( E ), L ) = 0 for every holomorphic line bundle L on P ( E ).

Journal

Georgian Mathematical Journalde Gruyter

Published: Mar 1, 2004

Keywords: Infinite-dimensional projective space; complex Banach manifold; holomorphic vector bundle; holomorphic line bundle; localizing Banach space; Banach space with countable unconditional basis

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