%0 Journal Article
%T The dimension of the space of Garnier equations with fixed locus of apparent singularities
%A Szilard Szabo
%J Mathematics
%D 2011
%I arXiv
%X 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 eigenvalues of the residue 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. We conclude that the family of such differential equations is of the expected dimension.
%U http://arxiv.org/abs/1102.3858v1