Abundance Conjecture

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Abundance Conjecture

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dc.contributor.author Siu, Yum-Tong
dc.date.accessioned 2011-11-09T15:37:25Z
dc.date.issued 2010
dc.identifier.citation Siu, Yum-Tong. 2010. Abundance conjecture. In Geometry and analysis, no. 2, edited by Lizhen Ji, 271-317. Advanced Lectures in Mathematics. Boston: International Press. en_US
dc.identifier.isbn 978-1-57146-225-1 en_US
dc.identifier.issn 0932-7134 en_US
dc.identifier.uri http://nrs.harvard.edu/urn-3:HUL.InstRepos:5343170
dc.description.abstract We sketch a proof of the abundance conjecture that the Kodaira dimension of a compact complex algebraic manifold equals its numerical Kodaira dimension. The proof consists of the following three parts: (i) the case of numerical Kodaira dimension zero, (ii) the general case under the assumption of the coincidence of the numerically trivial foliation and fibration for the canonical bundle, and (iii) the verification of the coincidence of the numerically trivial foliation and fibration for the canonical bundle. Besides the use of standard techniques such as the L2 estimates of d-bar, the first part uses Simpson's method of replacing the flat line bundle in a nontrivial flatly twisted canonical section by a torsion flat line bundle. Simpson's method relies on the technique of Gelfond-Schneider for the solution of the seventh problem of Hilbert. The second part uses the semi-positivity of the direct image of a relative pluricanonical bundle. The third part uses the technique of the First Main Theorem of Nevanlinna theory and its use is related to the technique of Gelfond-Schneider in the first part. en_US
dc.description.sponsorship Mathematics en_US
dc.language.iso en_US en_US
dc.publisher International Press en_US
dash.license OAP
dc.subject algebraic geometry en_US
dc.title Abundance Conjecture en_US
dc.type Monograph or Book en_US
dc.description.version Accepted Manuscript en_US
dc.relation.journal Advanced Lectures in Mathematics en_US
dash.depositing.author Siu, Yum-Tong
dc.date.available 2011-11-09T15:37:25Z

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  • FAS Scholarly Articles [7213]
    Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University

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