Orbifold-uniformizing differential equations. III: Arrangements defined by 3-dimensional primitive unitary reflection groups
type: Item
instance of: scholarly article
title: Orbifold-uniformizing differential equations. III: Arrangements defined by 3-dimensional primitive unitary reflection groups
zbMATH Open document ID: 0579.58025
DOI: 10.1007/BF01457077
author: Masaaki Yoshida
published in: Mathematische Annalen
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164102
review text: [For part I see ibid. 267, 125-142 (1984; Zbl 0521.58052; for part II see the preceding review Zbl 0579.58024] Let G be a 3-dimensional primitive unitary reflection group and A be the line arrangement on the complex projective plane X defined by the group G. For each group G, G-invariant Fuchsian systems E of linear differential equations of rank \((=the\) dimension of the solution space) three with regular singularities along A are constructed. In general, a system of rank 3 on X (with inhomogeneous coordinates \(y^ 1, y^ 2)\) is represented by a tensor \[ \omega =\sum P_{ijk} dy^ i\otimes dy^ j\otimes dy^ k(dy^ 1\wedge dy^ 2)^{-1}. \] If \(p: {\mathbb{C}}^ 3-\{0\}\to X\) denotes the natural projection \((x^ 0,x^ 1,x^ 2)\to (y^ 1=x^ 1/x^ 0\), \(y^ 2=x^ 2/x^ 0)\), the associate form \(p^*\omega\) to E is explicitly expressed as G-invariant symmetric 3-form.
Mathematics Subject Classification ID: 37C80
Mathematics Subject Classification ID: 57S30
Mathematics Subject Classification ID: 51F15
Mathematics Subject Classification ID: 51H30
zbMATH DE Number: 3927954
zbMATH Keywords: primitive unitary reflection group
zbMATH Keywords: G-invariant Fuchsian systems E of linear differential equations
MaRDI profile type: Publication
cites work: Chern numbers of algebraic surfaces
cites work: Finite Unitary Reflection Groups
cites work: ORBIFOLD-UNIFORMIZING DIFFERENTIAL EQUATIONS II
cites work: Canonical forms of some systems of linear partial differential equations
cites work: A NOTE ON ORBIFOLD-UNIFORMIZING DIFFERENTIAL EQUATIONS
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description: scientific article; zbMATH DE number 3927954