The θ-density in Arakelov geometry

2021/06/06 by Xiaozong Wang, Wang, Xiaozong
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2106.03123

openalex publication_date 2021/06/06 · openalex created_date 2021/06/22 · openalex updated_date 2026/07/28

Abstract

In this article, we construct a θ-density for the global sections of ample Hermitian line bundles on a projective arithmetic variety. We show that this density has similar behaviour to the usual density in the Arakelov geometric setting, where only global sections of norm smaller than 1 are considered. In particular, we prove the analogue by θ-density of two Bertini kind theorems, on irreducibility and regularity respectively.

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