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Abstract <p> We introduce and study the notion of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11501_2025_8536_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(G\)</EquationSource> </InlineEquation>-coregularity of algebraic varieties endowed with an action of a finite group <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11501_2025_8536_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(G\)</EquationSource> </InlineEquation>. We compute the <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11501_2025_8536_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(G\)</EquationSource> </InlineEquation>-coregularity of smooth del Pezzo surfaces of degree at least <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11501_2025_8536_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(6\)</EquationSource> </InlineEquation>, and give a characterization of groups that can act on conic bundles with <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11501_2025_8536_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(G\)</EquationSource> </InlineEquation>-coregularity <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11501_2025_8536_Article_IEq7.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(0\)</EquationSource> </InlineEquation>. We describe the relations between the notions of <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11501_2025_8536_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(G\)</EquationSource> </InlineEquation>-coregularity, <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11501_2025_8536_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(G\)</EquationSource> </InlineEquation>-log canonical thresholds, <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11501_2025_8536_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(G\)</EquationSource> </InlineEquation>-birational rigidity, and exceptional quotient singularities. </p>

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\(G\)-Coregularity of del Pezzo Surfaces

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • Konstantin Loginov,
  • Victor Przyjalkowski,
  • Andrey Trepalin

摘要

Abstract

We introduce and study the notion of \(G\) -coregularity of algebraic varieties endowed with an action of a finite group \(G\) . We compute the \(G\) -coregularity of smooth del Pezzo surfaces of degree at least \(6\) , and give a characterization of groups that can act on conic bundles with \(G\) -coregularity \(0\) . We describe the relations between the notions of \(G\) -coregularity, \(G\) -log canonical thresholds, \(G\) -birational rigidity, and exceptional quotient singularities.