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 $$1/k-1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mi>k</mml:mi> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> . We provide a concrete classification algorithm for fixed k and give explicit results for $$k=1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> , 2 and 3. This comprises in particular the cases of Gorenstein index 1, 2 and 3.