Flat semigroups and weighted homogeneous surface singularities

Baja, Zsolt and László, Tamás (2025) Flat semigroups and weighted homogeneous surface singularities. ALGEBRAIC AND GEOMETRIC TOPOLOGY. ISSN 1472-2739 (In Press)

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Abstract

We consider numerical semigroups associated with normal weighted homogeneous surface singularities with rational homology sphere links. We say that a semigroup is representable if it can be realized in this way. In this article we characterize the representable semigroups by proving that they are exactly those semigroups which can be written as a quotient of a flat semigroup. As an intermediate step, we study the class of flat semigroups and show that they can be represented by a special subclass of isolated complete intersection singularities whose defining equations can be given explicitely.

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