Lattice Polygons and Surfaces with Torus Action

Abstract

This thesis contributes to the classification of log del Pezzo surfaces with torus action. Such a surface is 1/k-log canonical if all discrepancies of a resolution of singularities are greater than or equal to -1+1/k. We present an explicit classification strategy for fixed k as well as the concrete results in the cases k=1,2,3. [untranslated]