The Proportion of Weierstrass Semigroups

Details The Proportion of Weierstrass Semigroups The Proportion of Weierstrass Semigroups

2012-02-28

arxiv.org/abs/1202.6331v1

Mathematics

Combinatorics

15 pages, submitted

Scientific paper

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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