Artin-Schreier coverings of algebraic surfaces
Let k be an algebraically closed field of characteristic \(p>0\) and let X be a nonsingular projective surface over k. An \textit{Artin-Schreier covering} is a finite morphism \(\pi: Y\to X\) from a normal surface Y onto X such that the field extension \(k(Y)/k(X)\) is an Artin-Schreier extension, i.e., \(k(Y)/k(X)\) is a Galois extension whose Galois group is isomorphic to \({\mathbb{Z}}/p{\mathbb{Z}}.\) A good class of Artin-Schreier coverings which is called \textit{of simple type} is defined and, in the case of simple type, some formulas are given to compute invariants of coverings. Moreover, smooth Artin-Schreier coverings of simple type with ample branch loci are determined.
scientific article; zbMATH DE number 4144115
scientific article