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<p>A variety is said to satisfy Condition <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((\textbf{A})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="bold">A</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> if every finite abelian subgroup of its automorphism group has a fixed point. We show that a smooth Fano 3-fold not satisfying Condition&#xa0;<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((\textbf{A})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="bold">A</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> is K-polystable unless it is contained in eight exceptional deformation families (seven of them consist of one smooth member, and one of them has two-parameter moduli).</p>

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K-stability of Fano 3-folds in the World of Null-A

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月8日

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  • Hamid Abban,
  • Ivan Cheltsov,
  • Takashi Kishimoto,
  • Frédéric Mangolte

摘要

A variety is said to satisfy Condition \((\textbf{A})\) ( A ) if every finite abelian subgroup of its automorphism group has a fixed point. We show that a smooth Fano 3-fold not satisfying Condition  \((\textbf{A})\) ( A ) is K-polystable unless it is contained in eight exceptional deformation families (seven of them consist of one smooth member, and one of them has two-parameter moduli).