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<p>Given a projective morphism <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(f:X\rightarrow Y\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mo>:</mo> <mi>X</mi> <mo stretchy="false">→</mo> <mi>Y</mi> </mrow> </math></EquationSource> </InlineEquation> from a complex space to a complex manifold, we prove the Griffiths semi-positivity and minimal extension property of the direct image sheaf <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(f_*(\mathscr {F})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>f</mi> <mrow> <mrow /> <mo>∗</mo> </mrow> </msub> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="script">F</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. Here, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathscr {F}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">F</mi> </math></EquationSource> </InlineEquation> is a coherent sheaf on <i>X</i>, which consists of the Grauert-Riemenschneider dualizing sheaf, a multiplier ideal sheaf, and a variation of Hodge structure (or more generally, a tame harmonic bundle).</p>

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Minimal Extension Property of Direct Images

  • 期刊论文

  • 发表日期：

    2026年4月10日

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  • Chen Zhao

摘要

Given a projective morphism \(f:X\rightarrow Y\) f : X → Y from a complex space to a complex manifold, we prove the Griffiths semi-positivity and minimal extension property of the direct image sheaf \(f_*(\mathscr {F})\) f ∗ ( F ) . Here, \(\mathscr {F}\) F is a coherent sheaf on X, which consists of the Grauert-Riemenschneider dualizing sheaf, a multiplier ideal sheaf, and a variation of Hodge structure (or more generally, a tame harmonic bundle).