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<p>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.</p>

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An analytic proof of Griffiths’ conjecture on compact Riemann surfaces

  • 期刊论文

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  • 发表日期：

    2026年2月13日

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  • Rei Murakami

摘要

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.