The dimension of the space of Garnier equations with fixed locus of apparent singularities

Szabó Szilárd: The dimension of the space of Garnier equations with fixed locus of apparent singularities. In: Acta scientiarum mathematicarum, (79) 1-2. pp. 107-128. (2013)

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Abstract

We show that the conditions imposed on a second order linear differential equation with rational coefficients on the complex line by requiring it to have regular singularities with fixed exponents at the points of a finite set P and apparent singularities at a finite set Q (disjoint from P) determine a linear system of maximal rank. In addition, we show that certain auxiliary parameters can also be fixed. This enables us to conclude that the family of such differential equations is of the expected dimension and to define a birational map between an open subset of the moduli space of logarithmic connections with fixed logarithmic points and regular semi-simple residues and the Hilbert scheme of points on a quasi-projective surface.

Item Type:	Article
Journal or Publication Title:	Acta scientiarum mathematicarum
Date:	2013
Volume:	79
Number:	1-2
ISSN:	0001-6969
Page Range:	pp. 107-128
Language:	English
Contributors:	Contribution Name UNSPECIFIED Kurusa Árpád
Publisher:	Bolyai Institute, University of Szeged
Place of Publication:	Szeged
Official URL:	http://www.acta.hu
Related URLs:	http://acta.bibl.u-szeged.hu/38688/
Uncontrolled Keywords:	Matematika, Garnier-egyenletek
Additional Information:	Bibliogr.: 128. p. ; összefoglalás angol nyelven
Subjects:	01. Natural sciences 01. Natural sciences > 01.01. Mathematics
Date Deposited:	2016. Oct. 17. 10:38
Last Modified:	2026. Mar. 06. 11:36
URI:	http://acta.bibl.u-szeged.hu/id/eprint/30867

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