The authors establish that for algebraically integrable foliations on klt varieties, and for rank one foliations on threefolds, any two Mori fiber spaces are connected by Sarkisov links.
The Sarkisov program on log surfaces
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We show that the Sarkisov program holds for $\mathbb{Q}$-factorial log surfaces and log canonical surfaces over any algebraically closed field.
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Sarkisov program for algebraically integrable and threefold foliations
The authors establish that for algebraically integrable foliations on klt varieties, and for rank one foliations on threefolds, any two Mori fiber spaces are connected by Sarkisov links.