Peculiar Loci of Ample and Spanned Line Bundles
Algebraic Geometry
2007-05-23 v1
Abstract
The bad locus and the rude locus of an ample and base point free linear system on a smooth complex projective variety are introduced and studied. The bad locus is defined as the set of points that force divisors through them to be reducible. The rude locus is defined as the set of points such that divisors that are singular at them are forced to be reducible. The existence of a nonmempty bad locus is shown to be exclusively a two dimensional phenomenon. Polarized surfaces of small degree, or whose degree is the square of a prime, with nonempty bad loci are completely classified. Several explicit examples are offered to describe the variety of behaviors of the two loci.
Keywords
Cite
@article{arxiv.math/0306139,
title = {Peculiar Loci of Ample and Spanned Line Bundles},
author = {Gian Mario Besana and Sandra Di Rocco and Antonio Lanteri},
journal= {arXiv preprint arXiv:math/0306139},
year = {2007}
}
Comments
to appear in Manuscripta Mathematica