Representability of systems of proportionally modular numerical semigroups

Zsolt Baja; Tamás László; Zsuzsa Nagy

Representability of systems of proportionally modular numerical semigroups

Number Theory 2026-07-15 v1 Geometric Topology

Authors: Zsolt Baja , Tamás László , Zsuzsa Nagy

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.

Keywords

proportionally modular numerical semigroups equivariant resolution weighted homogeneous surface singularity rational homology sphere quotient semigroups

Cite

@article{arxiv.2607.13619,
  title  = {Representability of systems of proportionally modular numerical semigroups},
  author = {Zsolt Baja and Tamás László and Zsuzsa Nagy},
  journal= {arXiv preprint arXiv:2607.13619},
  year   = {2026}
}

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12 pages