Sarkisov Program for algebraically integrable adjoint foliated structures

Chen, Yifei, Liu, Jihao, Wang, Yanze

International Mathematics Research Notices, Volume 2026, Issue 6, March 2026

pdf slides url
Sarkisov Program for AFS, using double scaling.

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 $3$ with mild singularities. Log version and adjoint foliated version of the aforementioned Sarkisov programs are also established.

Bibtex

@article{10.1093/imrn/rnag045,
    author = {Chen, Yifei and Liu, Jihao and Wang, Yanze},
    title = {Sarkisov Program for Algebraically Integrable and Three-fold Foliations},
    journal = {International Mathematics Research Notices},
    volume = {2026},
    number = {6},
    pages = {rnag045},
    year = {2026},
    month = {03},
    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 \$3\$ with mild singularities. Log version and adjoint foliated version of the aforementioned Sarkisov programs are also established.},
    issn = {1073-7928},
    doi = {10.1093/imrn/rnag045},
    url = {https://doi.org/10.1093/imrn/rnag045},
    eprint = {https://academic.oup.com/imrn/article-pdf/2026/6/rnag045/67395230/rnag045.pdf},
}