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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 ).
Georgian Mathematical Journal – de 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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