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arXiv · 2607.13619

Representability of systems of proportionally modular numerical semigroups

Zsolt Baja·Tamás László·Zsuzsa Nagy
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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.

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Zsolt Baja, Tamás László, Zsuzsa Nagy. 2026-07-15. Representability of systems of proportionally modular numerical semigroups. https://arxiv.org/abs/2607.13619

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