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

Alexei Entin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

For a projective curve $C\subset \textbf{P} ^n$ defined over a finite field $\textbf{F} _q$ we study the statistics of the $\textbf{F} _q$-structure of a section of $C$ by a random hyperplane defined over $\textbf{F} _q$ in the $q\to \infty $ limit. We obtain a very general equidistribution result for this problem. We deduce many old and new results about decomposition statistics over finite fields in this limit. Our main tool will be the calculation of the monodromy of transversal hyperplane sections of a projective curve.

Original languageEnglish
Pages (from-to)10409-10441
Number of pages33
JournalInternational Mathematics Research Notices
Volume2021
Issue number14
DOIs
StatePublished - 1 Jul 2021

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