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<p>We establish the minimal model program (MMP) for generalized foliated threefolds <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((X, \mathcal {F}, B, \textbf{M})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo>,</mo> <mi mathvariant="script">F</mi> <mo>,</mo> <mi>B</mi> <mo>,</mo> <mi mathvariant="bold">M</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> of rank 1, extending the result of Cascini and Spicer in [<CitationRef CitationID="CR21">21</CitationRef>]. As an application of the generalized foliated MMP, we prove a base-point-free theorem for foliated triples on threefolds. We also prove the ACC for log canonical thresholds for generalized foliated threefolds of rank 1.</p>

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MMP for generalized foliated threefolds of rank one

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Mengchu Li

摘要

We establish the minimal model program (MMP) for generalized foliated threefolds \((X, \mathcal {F}, B, \textbf{M})\) ( X , F , B , M ) of rank 1, extending the result of Cascini and Spicer in [21]. As an application of the generalized foliated MMP, we prove a base-point-free theorem for foliated triples on threefolds. We also prove the ACC for log canonical thresholds for generalized foliated threefolds of rank 1.