The Proportion of Weierstrass Semigroups
arXiv:1202.6331 · doi:10.1016/j.jalgebra.2012.09.041
Abstract
We solve a problem of Komeda concerning the proportion of numerical semigroups which do not satisfy Buchweitz' necessary criterion for a semigroup to occur as the Weierstrass semigroup of a point on an algebraic curve. We also show that the family of semigroups known to be Weierstrass semigroups using a result of Eisenbud and Harris, has zero density in the set of all semigroups. In the process, we prove several more general results about the structure of a typical numerical semigroup.
15 pages. Corrected typos, some minors mathematical changes, added some discussion. To appear in J. Algebra