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<p>We consider log del Pezzo surfaces coming with a non-trivial torus action. Such a surface is 1/<i>k</i>-log canonical if it allows a resolution of singularities with discrepanies all greater than or equal to <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(1/k-1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo stretchy="false">/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. We provide a concrete classification algorithm for fixed <i>k</i> and give explicit results for <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(k=1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, 2 and 3. This comprises in particular the cases of Gorenstein index 1, 2 and 3.</p>

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Classifying log del Pezzo surfaces with torus action

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月22日

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  • Daniel Hättig,
  • Jürgen Hausen,
  • Justus Springer

摘要

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 \(1/k-1\) 1 / k - 1 . We provide a concrete classification algorithm for fixed k and give explicit results for \(k=1\) k = 1 , 2 and 3. This comprises in particular the cases of Gorenstein index 1, 2 and 3.