Analytic classification of the differential equations \(ydy + \dots = 0\) and moduli spaces. (Classification analytique d’équations différentielles \(ydy + \dots = 0\) et espace de modules.) (French) Zbl 0880.34002
A holomorphic 1-form on \(({\mathbb{C}}^2,0)\) with 1-jet \(y dy\) is formally conjugate with \(\Omega_\alpha^{n,p}=d(y^2+x^n)+x^p(\alpha+V(x)) dy\). One is interested in the analytic classification of germs with the same formal normal form. In case \(n<2p\) this was studied by D. Cerveau and R. Moussu [Bull. Soc. Math. Fr. 116, No. 4(1988), 459-488 (1989; Zbl 0696.58011)]. The present paper uses similar methods for \(p=2n\). It gives a precise description of the analytic conjugacy classes in terms of the holonomy of the singular foliation obtained by resolving the 1-form.
Reviewer: J.Stevens (Göteborg)
MSC:
| 34M05 | Entire and meromorphic solutions to ordinary differential equations in the complex domain |
| 32S65 | Singularities of holomorphic vector fields and foliations |
| 32G34 | Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation) |
Keywords:
projective holonomyCitations:
Zbl 0696.58011References:
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