3 papers
math.AG2026
The Number of Curves of Genus 2 with a Given Refined Humbert Invariant
Ernst Kani, Harun Kir
Let be a curve of genus 2 over an algebraically closed field . Every such curve comes equipped with a canonical quadratic form called its refined Humbert invariant.…
math.NT2026
The classification of the refined Humbert invariant for curves of genus 2
Harun Kir
The refined Humbert invariant is a positive definite quadratic form intrinsically attached to a curve of genus 2. This invariant is an algebraic generalization of the (usual) H…
math.NT2026
Constructing genus 2 curves with given refined Humbert invariants
Harun Kir
In 1994, Kani introduced an algebraic version of the Humbert invariant, known as the refined Humbert invariant. This invariant q_C is a positive definite quadratic form attached to…