On the number of parameters of linear differential equations with regular singularities on a compact Riemann surface (Q1109940)

The paper deals with the set V of all linear differential equations of order n on a compact Riemann surface X of genus g with regular singularities along a divisor Y of X consisting of m distinct points, provided \(m\geq 1\) or \(m\geq 2\) when \(g=0\). Using the theory of eulerian jet bundles the author proves the theorem of T. Saito that the affine space V has the dimension \(\cdot n(n+1)m+n^ 2(g-1).\)