Sarkisov 纲领（代数可积伴随叶层化结构）

陈亦飞, 刘济豪, 王延泽

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

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伴随叶层化结构的 Sarkisov 纲领，使用双尺度。

摘要

借助伴随叶层化结构的极小模型纲领理论，我们建立 klt 簇上代数可积叶层化的 Sarkisov 纲领：此类结构的任意两个 Mori 纤维空间由一列 Sarkisov 链环连接。结合 R. Mascharak 的结果，我们建立具有温和奇点的至多三维叶层化的 Sarkisov 纲领。上述 Sarkisov 纲领的对数版本与伴随叶层化版本亦被建立。

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},
}