Towards the Green-Griffiths-Lang conjecture via equivariant localisation

Abstract

The Green-Griffiths-Lang conjecture says that for every complex projective algebraic variety $X$ of general type there exists a proper algebraic subvariety of $X$ containing all nonconstant entire holomorphic curves $f:\mathbb{C}\to X$. Using equivariant localisation on the Demailly-Semple jet differentials bundle we give an affirmative answer to this conjecture for generic projective hypersurfaces $X\subset {\mathbb{P}}^{n+1}$ of degree $\mathrm{deg}(X)\ge n^{9n}$.

This paper is a rewritten version of the first part of arXiv:1011.4710/v1

References in corpus (4)

• Some recent transcendental techniques in algebraic and complex geometry
• Geometric invariant theory for graded unipotent groups and applications
• Projective completions of graded unipotent quotients
• Proof of the Kobayashi conjecture on the hyperbolicity of very general hypersurfaces

Cited by in corpus (3)

• Entire holomorphic curves into projective spaces intersecting a generic hypersurface of high degree
• On the Gauss maps of complete minimal surfaces in ${\mathbb{R}}^n$
• A remark on the intersection of plane curves