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

J. Travis Lee, Syracuse University

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.