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Splitting Of Vector Bundles On Punctured Spectrum Of Regular Local Rings, Mahdi Majidi-Zolbanin

Dissertations, Theses, and Capstone Projects

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 …