Monodromy of Hyperplane Sections of Curves and Decomposition Statistics\n over Finite Fields

2018/05/14 by Alexei Entin, Entin, Alexei · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1805.05454

openalex publication_date 2018/05/14 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

For a projective curve C\⊂\Pⁿ defined over \F_q we\nstudy the statistics of the \F_q-structure of a section of C by a\nrandom hyperplane defined over \F_q in the q\→\∞ limit. We\nobtain a very general equidistribution result for this problem. We deduce many\nold and new results about decomposition statistics over finite fields in this\nlimit. Our main tool will be the calculation of the monodromy of transversal\nhyperplane sections of a projective curve.\n

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