Robert Wilms

collaborators

3 papers

math.AG2026

A uniform lower bound for the Zhang-Kawazumi invariant and applications to the Bogomolov conjecture

Robert Wilms

We prove that the Zhang-Kawazumi invariant $φ (X)$ of a compact and connected Riemann surface $X$ of genus $g \geq 2$ is strictly larger than \[\frac{g(g+2)-(2g+1)H_g}{g-1},\] where $…

math.NT2026

On the Faltings height of the curve $y^{2} = x^{n} - 1$

Robert Wilms

We compute the stable Faltings height of the hyperelliptic curve $X_{n} : y^{2} = x^{n} - 1$ for every odd integer $n \geq 3$ in terms of special values of Euler's gamma function. In par…

math.AG2023

An alternative proof of the Faltings-Elkies bound

Robert Wilms

We give an alternative proof of the Faltings-Elkies bound on the average value of the Arakelov-Green function in pairs of a given set of $n$ points on a Riemann surface, which grow…

A uniform lower bound for the Zhang-Kawazumi invariant and applications to the Bogomolov conjecture

On the Faltings height of the curve y2=xn−1

An alternative proof of the Faltings-Elkies bound

On the Faltings height of the curve $y^{2} = x^{n} - 1$