Answers are grounded in this paper and cite their sources.
This article proposes to study the moduli space of a germ of curve S in the complex plane, that is to say the equisingularity class of S up to analytical equivalence relation. The first part is devoted to proving that this last quotient can be endowed with a reasonable, yet not canonical, complex structure. The second part deals with the computation of its generic dimension in terms of topological invariants of S. It can be obtained from the study of the valuations of the Saito module of S, Der(logS), i.e. the module of vector fields tangent to S.
No takes yet. Share an insight, caveat, or question.
Yohann Genzmer (2024) studied this question.
Synapse has enriched 10 related papers. Consider them for comparative context: