Wildly ramified actions and surfaces of general type arising from Artin–Schreier curves

Abstract

We analyse the diagonal quotient for the product of certain Artin--Schreier curves. The smooth models are almost always surfaces of general type, with Chern slopes tending asymptotically to 1. The calculation of numerical invariants relies on a close examination of the relevant wild quotient singularity in characteristic $p$. It turns out that the canonical model has $q-1$ rational double points of type $A_{q-1}$, and embeds as a divisor of degree $q$ in ${\mathbb{P}}^3$, which is in some sense reminiscent of the classical Kummer quartic.