Dimension of the moduli space of a curve in the complex plane

In this article, we prove a formula that computes the generic dimension of the moduli space of a germ of irreducible curve in the complex plane. It is obtained from the study of the Saito module associated to the curve, which is the module of germs of holomorphic 1-forms leaving the curve invariant.

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Bibliographic Details
Published in:International mathematics research notices 2022, Vol.2022 (5)
Main Author: Genzmer, Yohann
Format: Article
Language:English
Subjects:
Complex Variables
Dynamical Systems
Mathematics
Online Access:Get full text
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Description
Summary:In this article, we prove a formula that computes the generic dimension of the moduli space of a germ of irreducible curve in the complex plane. It is obtained from the study of the Saito module associated to the curve, which is the module of germs of holomorphic 1-forms leaving the curve invariant.
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rnaa237