Classifying log del Pezzo surfaces with torus action

Daniel Haettig; Juergen Hausen; Justus Springer

Classifying log del Pezzo surfaces with torus action

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arxiv 2302.03095 v1 pith:3YLJOJZE submitted 2023-02-06 math.AG

Daniel Haettig , Juergen Hausen , Justus Springer This is my paper · ORCID

classification math.AG

keywords actionpezzosurfacestorusalgorithmallowscanonicalcases

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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 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.

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