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arXiv · 1202.6331

The Proportion of Weierstrass Semigroups

Nathan Kaplan·Lynnelle Ye
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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.

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Nathan Kaplan, Lynnelle Ye. 2012-10-29. The Proportion of Weierstrass Semigroups. https://doi.org/10.1016/j.jalgebra.2012.09.041

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