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Boundedness of minimal partial du Val resolutions of canonical surface foliations

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arxiv 1912.02931 v3 pith:KC4UV6CV submitted 2019-12-06 math.AG

Yen-An Chen This is my paper · ORCID
classification math.AG
keywords boundednesscanonicalfoliatedgeneralmathscrminimalmodelspartial
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abstract

In this paper, we prove the boundedness of foliated surfaces $(X,\mathscr{F})$ which are minimal partial du Val resolutions of canonical models $(X_c,\mathscr{F}_c)$ of general type. For applications, we show the boundedness of non-cusp singularities on canonical models of foliated surfaces of general type and the effective generation on the complement of the cusp singularities.

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  1. Foliated Minimal Models and Flops

    math.AG 2026-08 conditional novelty 8.0 of 10

    Rank one foliations with canonical singularities have unique minimal models; co-rank one threefolds admit D-flops in klt and F-dlt settings, while new examples show flops and canonical models can fail.

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