Robert Wilms

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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.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…