Explicit formulas and exact values for the number of rational points on singular curves over finite fields

Fuente: arXiv
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Main Author: Beninati, Lorenzo
Format: Preprint
Published: 2026
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author Beninati, Lorenzo
author_facet Beninati, Lorenzo
contents We provide new explicit formulas for bounding the number of rational points on singular curves over finite fields. This enables us to obtain exact values of N q (g, $π$) which is defined as the maximum number of rational points over F q on a curve of geometric genus g and arithmetic genus $π$. We also give special attention to the case g = 2 in order to extend the work of Aubry and Iezzi on N q (0, $π$) and N q (1, $π$).
format Preprint
id arxiv_https___arxiv_org_abs_2602_19781
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Explicit formulas and exact values for the number of rational points on singular curves over finite fields
Beninati, Lorenzo
Algebraic Geometry
We provide new explicit formulas for bounding the number of rational points on singular curves over finite fields. This enables us to obtain exact values of N q (g, $π$) which is defined as the maximum number of rational points over F q on a curve of geometric genus g and arithmetic genus $π$. We also give special attention to the case g = 2 in order to extend the work of Aubry and Iezzi on N q (0, $π$) and N q (1, $π$).
title Explicit formulas and exact values for the number of rational points on singular curves over finite fields
topic Algebraic Geometry
url https://arxiv.org/abs/2602.19781