The Proportion of Weierstrass Semigroups
Combinatorics
2017-06-13 v2 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.1202.6331,
title = {The Proportion of Weierstrass Semigroups},
author = {Nathan Kaplan and Lynnelle Ye},
journal= {arXiv preprint arXiv:1202.6331},
year = {2017}
}
Comments
15 pages. Corrected typos, some minors mathematical changes, added some discussion. To appear in J. Algebra