Degenerate Riemann-Hilbert-Birkhoff problems, semisimplicity, and convergence of WDVV-potentials
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2020
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910627659776000 |
|---|---|
| author | Cotti, Giordano |
| author_facet | Cotti, Giordano |
| contents | In the first part of this paper, we give a new analytical proof of a theorem of C. Sabbah on integrable deformations of meromorphic connections on $\mathbb P^1$ with coalescing irregular singularities of Poincaré rank 1, and generalizing a previous result of B. Malgrange. In the second part of this paper, as an application, we prove that any semisimple formal Frobenius manifold (over $\mathbb C$), with unit and Euler field, is the completion of an analytic pointed germ of a Dubrovin-Frobenius manifold. In other words, any formal power series, which provides a quasi-homogenous solution of WDVV equations and defines a semisimple Frobenius algebra at the origin, is actually convergent under no further tameness assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_04498 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Degenerate Riemann-Hilbert-Birkhoff problems, semisimplicity, and convergence of WDVV-potentials Cotti, Giordano Differential Geometry Mathematical Physics Algebraic Geometry 53D45, 34M40, 34M50, 34M56 In the first part of this paper, we give a new analytical proof of a theorem of C. Sabbah on integrable deformations of meromorphic connections on $\mathbb P^1$ with coalescing irregular singularities of Poincaré rank 1, and generalizing a previous result of B. Malgrange. In the second part of this paper, as an application, we prove that any semisimple formal Frobenius manifold (over $\mathbb C$), with unit and Euler field, is the completion of an analytic pointed germ of a Dubrovin-Frobenius manifold. In other words, any formal power series, which provides a quasi-homogenous solution of WDVV equations and defines a semisimple Frobenius algebra at the origin, is actually convergent under no further tameness assumptions. |
| title | Degenerate Riemann-Hilbert-Birkhoff problems, semisimplicity, and convergence of WDVV-potentials |
| topic | Differential Geometry Mathematical Physics Algebraic Geometry 53D45, 34M40, 34M50, 34M56 |
| url | https://arxiv.org/abs/2011.04498 |