Codimension and connectedness of degeneracy loci over local rings

Abstract

We deduce results on the dimension and connectedness of degeneracy loci of maps of finite modules $f:M\to N$ over a local noetherian ring $(A,\mathfrak{m})$. We show for instance that the expected determinantal bounds on the dimension of the t-$th$ degeneracy locus of $f$ hold if $f\in \mathfrak{m}Hom(M,N)$, and that this degeneracy locus is connected in the expected dimension provided $\hat{A}$ is a domain.

17 pages