Holomorphic functions on bundles over annuli

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dc.contributor.authorZaffran, Danko
dc.date.accessioned2013-03-06T22:06:15Z-
dc.date.available2013-03-06T22:06:15Z-
dc.date.created2012-02-06-
dc.date.created2012-02-06-
dc.date.issued2008-08-
dc.identifier.citationMATHEMATISCHE ANNALEN, v.341, no.4, pp.717 - 733-
dc.identifier.issn0025-5831-
dc.identifier.urihttp://hdl.handle.net/10203/88627-
dc.description.abstractWe consider a family {E-m( D, M)} of holomorphic bundles constructed as follows: from any given M is an element of GL(n)(Z), we associate a "multiplicative automorphism" phi of (C*)(n). Now let D subset of (C*)(n) be phi-invariant Stein Reinhardt domain. Then E-m(D, M) is defined as the flat bundle over the annulus of modulus m > 0, with fiber D, and monodromy phi. We show that the function theory on E-m(D, M) depends nontrivially on the parameters m, M and D. Our main result is that E-m(D, M) is Stein if and only if m log.( M) <= 2 pi(2), where rho(M) denotes the max of the spectral radii of M and M-1. As corollaries, we: (1) obtain a classification result for Reinhardt domains in all dimensions; (2) establish a similarity between two known counterexamples to a question of J.-P. Serre; and (3) suggest a potential reformulation of a disproved conjecture of Siu Y.-T.-
dc.languageEnglish-
dc.publisherSPRINGER-
dc.subjectFIBER-BUNDLES-
dc.subjectSERRE PROBLEM-
dc.subjectBOUNDED DOMAIN-
dc.subjectBASE-
dc.titleHolomorphic functions on bundles over annuli-
dc.typeArticle-
dc.identifier.wosid000256322100001-
dc.identifier.scopusid2-s2.0-44449121709-
dc.type.rimsART-
dc.citation.volume341-
dc.citation.issue4-
dc.citation.beginningpage717-
dc.citation.endingpage733-
dc.citation.publicationnameMATHEMATISCHE ANNALEN-
dc.identifier.doi10.1007/s00208-007-0201-4-
dc.contributor.localauthorZaffran, Dan-
dc.type.journalArticleArticle-
dc.subject.keywordPlusFIBER-BUNDLES-
dc.subject.keywordPlusSERRE PROBLEM-
dc.subject.keywordPlusBOUNDED DOMAIN-
dc.subject.keywordPlusBASE-
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