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<p>We show that a compact Kähler manifold <i>M</i> containing a smooth connected divisor <i>D</i> such that <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(M \setminus D\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>M</mi> <mo lspace="0.15em" rspace="0.15em" stretchy="false">\</mo> <mi>D</mi> </mrow> </math></EquationSource> </InlineEquation> is a homology cell, e.g., contractible, must be projective space with <i>D</i> a hyperplane, provided <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\dim M \not \equiv 3 \pmod 4\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>dim</mo> <mi>M</mi> <mo>≢</mo> <mn>3</mn> <mspace width="4.44443pt" /> <mo stretchy="false">(</mo> <mo>mod</mo> <mspace width="0.277778em" /> <mn>4</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. This answers conjectures of Fujita in these dimensions.</p>

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Compactification of homology cells, Fujita’s conjectures and the complex projective space

  • 期刊论文

  • 发表日期：

    2026年2月13日

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  • Ping Li,
  • Thomas Peternell

摘要

We show that a compact Kähler manifold M containing a smooth connected divisor D such that \(M \setminus D\) M \ D is a homology cell, e.g., contractible, must be projective space with D a hyperplane, provided \(\dim M \not \equiv 3 \pmod 4\) dim M ≢ 3 ( mod 4 ) . This answers conjectures of Fujita in these dimensions.