MMP for co-rank one foliations on threefolds

@article{Cascini2018MMPFC,
  title={MMP for co-rank one foliations on threefolds},
  author={Paolo Cascini and Calum Spicer},
  journal={arXiv: Algebraic Geometry},
  year={2018}
}
We prove existence of flips, special termination, the base point free theorem and, in the case of log general type, the existence of minimal models for F-dlt foliated log pairs of co-rank one on a projective threefold. As applications, we show the existence of F-dlt modifications and F-terminalisations for foliated log pairs and we show that foliations with canonical or F-dlt singularities admit non-dicritical singularities. Finally, we show abundance in the case of numerically trivial… 
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15 Citations
Background Citations
3
Methods Citations
1

15 Citations

Local and global applications of the Minimal Model Program for co-rank one foliations on threefolds
We show that the Minimal Model Program for co-rank one foliations on threefolds terminates by proving foliation flips terminate. Moreover, we recover a full suite of powerful results on the…
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Log canonical models of foliated surfaces
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We present a variant of the classical Darboux-Jouanolou Theorem. Our main result provides a characterization of foliations which are pull-backs of foliations on surfaces by rational maps. As an…
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