AI 中文总结
研究比例模数值半群系统的可表示性问题，核心方法是从其商描述出发，通过双生成元数值半群实现每个商，再用双分支典范等变分解图及合适重数胶合，主要贡献是证明其可由特定加权齐次曲面奇点的分解表示。
AI 中文摘要
在本简短笔记中，我们证明了每个比例模数值半群系统都可由具有有理同调球面链的加权齐次曲面奇点的典范等变分解来表示。构造从比例模数值半群由双生成元数值半群的商描述开始，通过双分支典范等变分解图实现每个商，然后用合适的重数将这些图胶合起来。
英文摘要
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.
Comments12 pages
