Sarkisov program for algebraically integrable and threefold foliations
Yifei Chen, Jihao Liu, Yanze Wang
TL;DR
This paper extends the Sarkisov program to algebraically integrable foliations on klt varieties and threefolds, using the minimal model program, connecting Mori fiber spaces via Sarkisov links and handling mild singularities.
Contribution
It establishes the Sarkisov program for algebraically integrable foliations on klt varieties and threefolds, including log and adjoint foliated versions, using minimal model techniques.
Findings
Sarkisov links connect Mori fiber spaces of algebraically integrable foliations.
The program is extended to threefolds with mild singularities.
Log and adjoint foliated versions are also developed.
Abstract
By applying the theory of the minimal model program for adjoint foliated structures, we establish the Sarkisov program for algebraically integrable foliations on klt varieties: any two Mori fiber spaces of such structure are connected by a sequence of Sarkisov links. Combining with a result of R. Mascharak, we establish the Sarkisov program for foliations in dimension at most with mild singularities. Log version and adjoint foliated version of the aformentioned Sarkisov programs are also established.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Numerical methods for differential equations · Differential Equations and Numerical Methods