Work

An analytic proof of Griffiths’ conjecture on compact Riemann surfaces

Year: 2026

Type: article

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.

Source: Mathematische Annalen

DOI: 10.1007/s00208-026-03360-5

Author: Rei Murakami

Institution: Tohoku University

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Japan Society for the Promotion of Science