Dimension of the Moduli Space of a Germ of Curve in ℂ2-Reference-Cited by-同舟云学术

Dimension of the Moduli Space of a Germ of Curve in ℂ2

Published:2020-09-23 Issue: Volume: Page:
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Genzmer Yohann¹

Affiliation:

1. Institut de Mathématiques de Toulouse, 118 Route de Narbonne, 31062 Toulouse, France

Abstract

Abstract 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.

Funder

ANR

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/advance-article-pdf/doi/10.1093/imrn/rnaa237/33780523/rnaa237.pdf

Reference27 articles.

1. On the solutions of analytic equations;Artin;Invent. Math.,1968

2. Le nombre de modules du germe de courbe plane ${x}^a+{y}^b=0$;Briançon;Math. Ann.,1988

3. Invariant varieties through singularities of holomorphic vector fields;Camacho;Ann. of Math. (2),1982

4. Sur les modules des singularités des courbes planes;Delorme;Bull. Soc. Math. France,1978

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