On the locus of higher order jets of entire curves in complex projective\n varieties

2021/06/11 by Jean-Pierre Demailly, Demailly, Jean-Pierre
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2106.06388

openalex publication_date 2021/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a given complex projective variety, the existence of entire curves is\nstrongly constrained by the positivity properties of the cotangent bundle. The\nGreen-Griffiths-Lang conjecture stipulates that entire curves drawn on a\nvariety of general type should all be contained in a proper algebraic\nsubvariety. We present here new results on the existence of differential\nequations that strongly restrain the locus of entire curves in the general\ncontext of foliated or directed varieties, under appropriate positivity\nconditions.\n

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