Wildly ramified actions and surfaces of general type arising from Artin-Schreier curves. (English) Zbl 1317.14090

Ito, Hiroyuki; Schröer, Stefan

Faber, Carel (ed.) et al., Geometry and arithmetic. Based on the conference, Island of Schiermonnikoog, Netherlands, September 2010. Zürich: European Mathematical Society (EMS) (ISBN 978-3-03719-119-4/hbk). EMS Series of Congress Reports, 213-241 (2012).

Summary: 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.
For the entire collection see [Zbl 1253.00019].

MSC:

14J29	Surfaces of general type
14B05	Singularities in algebraic geometry

Keywords:

wild quotient singularities; surfaces of general type; Artin-Schreier coverings