On the Bertini regularity theorem for arithmetic varieties

2020/02/25 by Xiaozong Wang, Wang, Xiaozong
Mathematics · Social Sciences · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Vietnamese History and Culture Studies

paper · pdf · doi:10.48550/arxiv.2002.11179

openalex publication_date 2020/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a regular projective arithmetic variety equipped with an ample hermitian line bundle L. We prove that the proportion of global sections σ with ‖ σ‖_∞<1 of L^{⊗ d} whose divisor does not have a singular point on the fiber X_p over any prime p

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