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.
Higher dimensional foliated Mori theory
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abstract
We develop some basic results in a higher dimensional foliated Mori theory, and show how these results can be used to prove a structure theorem for the Kleiman-Mori cone of curves in terms of the numerical properties of $K_{\mathcal{F}}$ for rank 2 foliations on threefolds. We also make progress toward realizing a minimal model program for rank 2 foliations on threefolds.
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math.AG 1years
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.