Hyperbolicity of varieties with big linear representation of π₁

2022/02/01 by Ruiran Sun, Sun, Ruiran
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2202.00196

openalex publication_date 2022/02/01 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We show the following algebraicity result for a complex projective variety X with big representation of π₁ into a semi-simple algebraic group: There exists a proper subvariety Z ⊂ X such that for any algebraic curve C, any holomorphic map γ: C → X with γ(C) \not⊂ Z is induced from an algebraic morphism. As an application, we prove pseudo-Brody hyperbolicity of certain varieties with big reductive representations of π₁.

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