Splitting of Vector Bundles on Punctured Spectrum of Regular Local Rings

<p>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 <em>Hⁱ(U, E</em>)_{2_i_n−3}, where <em>n</em> 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.</p> <p>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 (<em>R,</em> m) is a regular local ring of dimension at least five, p is a prime ideal of codimension two, and the ring Γ (<em>V, R/</em>p) is Gorenstein, where <em>V</em> is the open set Spec(<em>R/</em>p) − {m}, then <em>R/</em>p is a complete intersection.</p>

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor

The Graduate School and University Center of The City University of New York

Year dc:date.available

2005

Author dc:creator

• Majidi-Zolbanin, Mahdi

Advisor dc:contributor.advisor

• Lucien Szpiro

Committee members dc:contributor.committeemember

• Raymond Hoobler
• Alphonse Vasquez
• Ian Morrison

• Mathematics

Repository record dc:identifier

https://academicworks.cuny.edu/gc_etds/1765

OAI identifier oai:identifier

oai:academicworks.cuny.edu:gc_etds-2797