Normal forms for ordinary differential operators, III

Abstract

In this paper, which is a follow-up of our first paper "Normal forms for ordinary differential operators, I", we extend the explicit parametrisation of torsion free rank one sheaves on projective irreducible curves with vanishing cohomology groups obtained earlier to analogous parametrisation of torsion free sheaves of arbitrary rank with vanishing cohomology groups on projective irreducible curves. As an illustration of our theorem we calculate one explicit example of such parametrisation, namely for rank two sheaves on a Weierstrass cubic curve.

40 p; V2: minor changes, to appear in Proc. Steklov Inst. Math. This is part 3 of a split version. For part 1, see arXiv:2406.14414v4