The Refined Humbert Invariant for an Automorphism Group of a Genus 2 Curve

2023/10/29 by Harun Kır, Kir, Harun · 1 citation
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2310.19076

openalex publication_date 2023/10/29 · openalex created_date 2023/11/01 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is to list the refined Humbert invariants for a given automorphism group of a curve C/K of genus 2 over an algebraically closed field K with characteristic 0. This invariant is an algebraic generalization of the (usual) Humbert invariant. It is a positive definite quadratic form associated to the curve C, and it encodes many geometric properties of the curve. The paper has a special interest in the cases where Aut(C)≃ D₄ or D₆. In these cases, several applications of the main results are discussed, including the curves with elliptic subcovers of a given degree.

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• Refined Humbert Invariants in Supersingular Isogeny Degree Analysis

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