The paper completes termination of the foliated minimal model program on threefolds and proves that terminal singularities admit first integrals and log canonical singularities admit separatrices.
Remarks about bubbles
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abstract
We make some remarks about bubbling on, not necessarily proper, champs de Deligne-Mumford, i.e. compactification of the space of mappings from a given (wholly scheme like) curve, so, in particular, on quasi-projective projective varieties. Under hypothesis on both the interior and the boundary such as Remark \ref{rmk:interior} below, this implies an optimal logarithmic variant of Mori's Bend-and-Break. The main technical remark is \ref{thm:logMM}, while our final remark, the cone theorem, \ref{rmk:cone}, is a variant.
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2019 1verdicts
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Local and global applications of the Minimal Model Program for co-rank one foliations on threefolds
The paper completes termination of the foliated minimal model program on threefolds and proves that terminal singularities admit first integrals and log canonical singularities admit separatrices.