On the singularities of effective loci of line bundles

Abstract

We prove that every irreducible component of semi-regular loci of effective line bundles in the Picard scheme of a smooth projective variety has at worst rational singularities. This generalizes Kempf's result on rational singularities of $W^0_d$ for smooth curves. We also work out an example of such loci for a ruled surface.

title is changed slightly, section 3 is almost rewritten, and an error in Corollary 2.14 is corrected