An analytic proof of Griffiths' conjecture on compact Riemann surfaces

Rei Murakami

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arXiv · 2509.23201

An analytic proof of Griffiths' conjecture on compact Riemann surfaces

Rei Murakami

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Abstract

Griffiths' conjecture asserts that a holomorphic vector bundle is ample if and only if it admits a Hermitian metric with positive curvature. In this paper, we present a new proof of this conjecture on compact Riemann surfaces using a system of PDEs introduced by Demailly. Our argument combines techniques developed by Uhlenbeck-Yau for Hermitian-Einstein metrics with Pingali's reduction of the problem to an a priori estimate.

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Rei Murakami. 2025-09-27. An analytic proof of Griffiths' conjecture on compact Riemann surfaces. https://arxiv.org/abs/2509.23201

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