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<p>For an affine <i>T</i>-variety <i>X</i> with the action of a torus <i>T</i>, this paper provides a combinatorial description of <i>X</i> with respect to the action of a subtorus <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12044_2024_811_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">\(T' \subset T\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>T</mi> <mo>′</mo> </msup> <mo>⊂</mo> <mi>T</mi> </mrow> </math></EquationSource> </InlineEquation> by showing that the (GIT constructed) pp-divisor constructed by Altmann and Hausen is <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12044_2024_811_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">\(T/T'\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>T</mi> <mo stretchy="false">/</mo> <msup> <mi>T</mi> <mo>′</mo> </msup> </mrow> </math></EquationSource> </InlineEquation>-invariant. We also describe the corresponding GIT fan.</p>

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Torus invariant pp-divisor using GIT

  • 期刊论文

  • 发表日期：

    2025年3月25日

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  • Pavankumar Dighe,
  • Vivek Mohan Mallick

摘要

For an affine T-variety X with the action of a torus T, this paper provides a combinatorial description of X with respect to the action of a subtorus \(T' \subset T\) T ′ ⊂ T by showing that the (GIT constructed) pp-divisor constructed by Altmann and Hausen is \(T/T'\) T / T ′ -invariant. We also describe the corresponding GIT fan.