The Demailly system for a direct sum of ample line bundles on Riemann surfaces

Abstract

We prove that a system of equations introduced by Demailly (to attack a conjecture of Griffiths) has a smooth solution for a direct sum of ample line bundles on a Riemann surface. We also reduce the problem for general vector bundles to an a priori estimate using Leray-Schauder degree theory.

Added a couple of remarks. Comments are most welcome