Classifying log del Pezzo surfaces with torus action

Abstract

We consider log del Pezzo surfaces coming with a non-trivial torus action. Such a surface is 1/k-log canonical if it allows a resolution of singularities with discrepanies all greater than or equal to 1/k-1. We provide a concrete classification algorithm for fixed k and give explicit results for k=1, 2 and 3. This comprises in particular the cases of Gorenstein index 1, 2 and 3.