# Geometry and Arithmetic

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#### DOI: 10.4171/119-1/13

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

Hiroyuki Ito[1] and Stefan Schröer[2]

(1) Tokyo University of Science, Chiba-Ken, Japan
(2) Heinrich-Heine-Universität, Düsseldorf, Germany

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.

Keywords: Wild quotient singularities, surfaces of general type, Artin–Schreier coverings