Title

An extension of the Thom-Porteous formula to a certain class of coherent sheaves

Date of Award

2004

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Electrical Engineering and Computer Science

Advisor(s)

Steven Diaz

Keywords

Coherent sheaves, Chow group, Degeneracy locus, Thom-Porteous formula

Subject Categories

Electrical and Computer Engineering

Abstract

Given a morphism σ of vector bundles E and F of rank e and f respectively over a purely n -dimensional scheme X , a nonnegative integer k ≤ min{ e , f }, and a degeneracy locus[Special characters omitted.] satisfying certain conditions, the Thom-Porteous formula gives the fundamental class of the degeneracy locus in the Chow group of X in terms of the Chern classes of E and F .

Recent work of S. Diaz suggests a method of extending this formula to morphisms of coherent sheaves that are not vector bundles. Given a morphism σ of coherent sheaves E and F over a nonsingular, integral, quasi-projective scheme X of dimension n ≥ 2 over a field K and a degeneracy locus as above satisfying certain conditions, this thesis derives an explicit formula for a class in the Chow group of X supported on the degeneracy locus.

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