Projective manifolds with small pluridegrees |
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Authors: | Mauro C Beltrametti Andrew J Sommese |
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Institution: | Dipartimento di Matematica, Università Degli Studi di Genova, Via Dodecaneso 35, I-16146 Genova, Italy ; Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556 |
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Abstract: | Let be a very ample line bundle on a connected complex projective manifold of dimension . Except for a short list of degenerate pairs , and there exists a morphism expressing as the blowup of a projective manifold at a finite set , with nef and big for the ample line bundle . The projective geometry of is largely controlled by the pluridegrees for , of . For example, , where is the genus of a curve section of , and is equal to the self-intersection of the canonical divisor of the minimal model of a surface section of . In this article, a detailed analysis is made of the pluridegrees of . The restrictions found are used to give a new lower bound for the dimension of the space of sections of . The inequalities for the pluridegrees, that are presented in this article, will be used in a sequel to study the sheet number of the morphism associated to . |
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Keywords: | Smooth complex polarized $n$-fold very ample line bundle adjunction theory log-general type pluridegrees |
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