Splitting of vector bundles on punctured spectrum of regular local rings.
Item
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Title
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Splitting of vector bundles on punctured spectrum of regular local rings.
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Identifier
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AAI3187456
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identifier
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3187456
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Creator
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Majidi-Zolbanin, Mahdi.
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Contributor
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Adviser: Lucien Szpiro
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Date
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2005
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Language
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English
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Publisher
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City University of New York.
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Subject
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Mathematics
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Abstract
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In this dissertation we study splitting of vector bundles of small rank on punctured spectrum of regular local rings. We give a splitting criterion for vector bundles of small rank in terms of vanishing of their intermediate cohomology modules Hi(U, E )2≤i≤ n-3, where n is the dimension of the regular local ring. This is the local analog of a result by N. Mohan Kumar, C. Peterson, and A. Prabhakar Rao for splitting of vector bundles of small rank on projective spaces.;As an application we give a positive answer (in a special case) to a conjecture of R. Hartshorne asserting that certain quotients of regular local rings have to be complete intersections. More precisely we prove that if ( R, m ) is a regular local ring of dimension at least five, p is a prime ideal of codimension two, and the ring Gamma( V, R/p&d15; ) is Gorenstein, where V is the open set Spec( R/ p ) - {lcub} m {rcub}, then R/ p is a complete intersection.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
