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<p>Consider <i>E</i> a vector bundle over a smooth curve <i>C</i>. We compute the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\delta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation>-invariant of all ample (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {Q}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">Q</mi> </math></EquationSource> </InlineEquation>-)line bundles on <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbb {P}(E)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="double-struck">P</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> when <i>E</i> is strictly Mumford semistable. We also investigate the case when one assumes that the Harder–Narasimhan filtration of <i>E</i> has only one step.</p>

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Delta-invariant for projective bundles over a curve and K-semistability

  • 期刊论文

  • 发表日期：

    2026年1月9日

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  • Houari Benammar Ammar,
  • Louis Massonnet,
  • Chenxi Yin

摘要

Consider E a vector bundle over a smooth curve C. We compute the \(\delta \) δ -invariant of all ample ( \(\mathbb {Q}\) Q -)line bundles on \(\mathbb {P}(E)\) P ( E ) when E is strictly Mumford semistable. We also investigate the case when one assumes that the Harder–Narasimhan filtration of E has only one step.