Poincaré series associated with surface singularities

2007/10/04 by András Némethi, Némethi, András · 1 citation
Mathematics · #32C35 #32S05 #32S25 #32S45 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.0710.0987

openalex publication_date 2007/10/04 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We unify and generalize formulas obtained by Campillo, Delgado and Gusein-Zade in their series of articles. Positive results are established for rational and minimally elliptic singularities. By examples and counterexamples we also try to find the `limits' of these identities. Connections with the Seiberg-Witten Invariant Conjecture and Semigroup Density Conjecture are discussed.

Cited by

• Delta invariant of ℚ-Cartier curve germs and the genus of representable numerical semigroups

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