Moduli space of complex structures
type: Item
instance of: scholarly article
title: Moduli space of complex structures
zbMATH Open document ID: 1191.32007
published in: Journal of Mathematical Sciences (New York)
publication date: 2010-01-19T00:00:00Z
review text: This paper is motivated by the understanding of configurations of points \(s_1,\dots, s_m\in \mathbb{P}^1(\mathbb{C})\), for which the Riemann-Hilbert monodromy problem admits solutions. For this, the author investigates connections between the following three spaces: the space of complex structures on the Riemann surface \(\mathbb{P}^1(\mathbb{C})\setminus\{s_1, \dots, s_m\}\), the space of Fuchsian systems of differential equations with singularities at the points \(\{s_1,\dots, s_m\}\) and the configuration space of \(n\)-gons in the three-dimensional space. He computes the Euler characteristics of the corresponding compactified manifolds with a method based on the signature formulas of the topological degree of a map. The author establishes a connection between the configuration of singular points for which the corresponding Riemann-Hilbert monodromly problem admits a solution and the configuration of singular points with no solution for Riemann-Hilbert problem.
reviewed by: Sorin Dumitrescu
Mathematics Subject Classification ID: 32G34
Mathematics Subject Classification ID: 32G15
Mathematics Subject Classification ID: 32S40
zbMATH DE Number: 5660089
zbMATH Keywords: Riemann-Hilbert monodromy problem
zbMATH Keywords: Fuchsian systems of differential equations
zbMATH Keywords: deformation of complex structures
author: Grigory Giorgadze
MaRDI profile type: Publication
full work available at URL: s10958-009-9522-z
OpenAlex ID: W2057642503
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DOI: 10.1007/S10958-009-9522-Z
description: scientific article; zbMATH DE number 5660089