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

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
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