Date of Degree

2005

Document Type

Dissertation

Degree Name

Ph.D.

Program

Mathematics

Advisor(s)

Lucien Szpiro

Committee Members

Raymond Hoobler

Alphonse Vasquez

Ian Morrison

Subject Categories

Mathematics

Abstract

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 Γ (V, R/p) is Gorenstein, where V is the open set Spec(R/p) − {m}, then R/p is a complete intersection.

Comments

Digital reproduction from the UMI microform.

Included in

Mathematics Commons

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