Wildly Ramified Actions and Surfaces of General Type Arising from Artin-Schreier Curves

TL;DR

This paper investigates surfaces of general type arising from Artin-Schreier curves, analyzing their quotient singularities, numerical invariants, and embeddings, revealing asymptotic Chern slope behavior and specific singularity types.

Contribution

It provides a detailed analysis of the quotient surfaces from Artin-Schreier curves, including their singularities, invariants, and embeddings, expanding understanding of surfaces in characteristic p.

Findings

Surfaces are mostly of general type with Chern slopes approaching 1.

Canonical models have q-1 rational double points of type A_{q-1}.

Surfaces embed as degree q divisors in P^3, similar to Kummer quartics.

Abstract

We analyse the diagonal quotient for products 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 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 P^3, which is in some sense reminiscent of the classical Kummer quartic.