On Griffiths conjecture
Xianjing Dong, Peichu Hu
TL;DR
This paper develops a new non-equidistribution theory for holomorphic curves in complex projective varieties and successfully proves the Griffiths and Green-Griffiths conjectures in Nevanlinna theory and algebraic geometry.
Contribution
It introduces a novel approach using holomorphic jets and Jacobian fields to prove longstanding conjectures in complex geometry.
Findings
Proved Griffiths conjecture.
Proved Green-Griffiths conjecture.
Established a new non-equidistribution theory.
Abstract
By using techniques of holomorphic jets and Jacobian fields, we devise a non-equidistribution theory of holomorphic curves into complex projective varieties intersecting normal crossing divisors. Based on this theory established, we prove the Griffiths conjecture and the Green-Griffiths conjecture in Nevanlinna theory and algebraic geometry.
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Taxonomy
TopicsMeromorphic and Entire Functions · Algebraic Geometry and Number Theory · Advanced Differential Equations and Dynamical Systems