Higher Order Bad Loci
arXiv:math/0702099
Abstract
Zero-schemes on smooth complex projective varieties, forcing all elements of ample and free linear systems to be reducible are studied. Relationships among the minimal length of such zero-schemes, the positivity of the line bundle associated with the linear system, and the dimension of the variety are established. A generalization to higher dimension subschemes is studied in the last section.
23 pages. Refereed version, to appear in JPAA