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