number theory

Representability of systems of proportionally modular numerical semigroups

arXiv:2607.13619

summary

The authors prove that any system of proportionally modular numerical semigroups can be represented by a canonical equivariant resolution of a weighted homogeneous surface singularity whose link is a rational homology sphere.

Abstract

In this short note we prove that every system of proportionally modular numerical semigroups is representable by a canonical equivariant resolution of a weighted homogeneous surface singularity with rational homology sphere link. The construction starts from the quotient descriptions of proportionally modular numerical semigroups by two-generator numerical semigroups, realizes each quotient by a two-legged canonical equivariant resolution graph, and then glues these graphs with suitable multiplicities.

12 pages

Topics & keywords

#numerical semigroups#proportionally modular#surface singularities#equivariant resolution#weighted homogeneousproportionally modular semigroupcanonical equivariant resolutionweighted homogeneous singularityquotient descriptiontwo-legged resolution graph
Representability of systems of proportionally modular numerical semigroups · wovepaper