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

2021/06/10 by Pingali, Vamsi Pritham · 1 citation
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2106.05775

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.

Cited by

• An analytic proof of Griffiths' conjecture on compact Riemann surfaces

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