Recent results on the Kobayashi and Green-Griffiths-Lang conjectures

DOI10.1007/s11537-019-1566-3zbMath1436.32086arXiv1801.04765OpenAlexW3003231064WikidataQ123011081 ScholiaQ123011081MaRDI QIDQ2303698

Jean-Pierre Demailly

Publication date: 4 March 2020

Published in: Japanese Journal of Mathematics. 3rd Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.04765

zbMATH Keywords

jet bundleLang conjecturejet metricKobayashi conjectureGreen-Griffiths conjecturejet differentialvariety of general typeKobayashi hyperbolic varietygenus of a curvedirected manifoldChern connection and curvaturenegativity of jet curvature

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Sheaves and cohomology of sections of holomorphic vector bundles, general results (32L10) Hyperbolic and Kobayashi hyperbolic manifolds (32Q45) Value distribution theory in higher dimensions (32H30) (n)-folds ((n>4)) (14J40)

Related Items (13)

Degrees \(d \geq \left (\sqrt{n} \log n\right)^n\) and \(d \geq \left (n \log n\right)^n\) in the conjectures of Green-Griffiths and of Kobayashi ⋮ On the hyperbolicity of base spaces for maximally variational families of smooth projective varieties (with an appendix by Dan Abramovich) ⋮ A Kobayashi and Bergman complete domain without bounded representations ⋮ Explicit computation of symmetric differentials and its application to quasihyperbolicity ⋮ Clustered families and applications to Lang‐type conjectures ⋮ Algebraic hyperbolicity of the very general quintic surface in \(\mathbb{P}^3\) ⋮ Families of explicit quasi-hyperbolic and hyperbolic surfaces ⋮ Algebraic hyperbolicity of very general surfaces ⋮ On the hyperbolicity of general hypersurfaces ⋮ A remark on the intersection of plane curves ⋮ On the locus of higher order jets of entire curves in complex projective varieties ⋮ Applications of a Grassmannian technique to hyperbolicity, Chow equivalency, and Seshadri constants ⋮ Hyperbolicity and specialness of symmetric powers

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