Flop between algebraically integrable foliations on potentially KLT varieties

Chen, Yifei, Liu, Jihao, Wang, Yanze

International Journal of Mathematics, 36(11):2550035, 2025

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Two minimal models of two MMPs from one lc AI AFS are connected by flops.

Abstract

We prove that for any two minimal models of an lc algebraically integrable foliated triple on potentially klt varieties, there exist small birational models that are connected by a sequence of flops. In particular, any two minimal models of lc algebraically integrable foliated triples on $\mathbb{Q}$-factorial klt varieties are connected by a sequence of flops. We also discuss the connection between minimal models for possibly non-algebraically integrable foliations on threefolds, assuming the minimal model program for generalized foliated quadruples.

Bibtex

@article{CLW25,
	title = {Flop between algebraically integrable foliations on potentially {KLT} varieties},
	volume = {36},
	issn = {0129-167X},
	url = {https://www.worldscientific.com/doi/10.1142/S0129167X25500351},
	doi = {10.1142/S0129167X25500351},
	abstract = {We prove that for any two minimal models of an lc algebraically integrable foliated triple on potentially klt varieties, there exist small birational models that are connected by a sequence of flops. In particular, any two minimal models of lc algebraically integrable foliated triples on 
Q-factorial klt varieties are connected by a sequence of flops. We also discuss the connection between minimal models for possibly non-algebraically integrable foliations on threefolds, assuming the minimal model program for generalized foliated quadruples.},
	number = {11},
	urldate = {2026-01-20},
	journal = {International Journal of Mathematics},
	publisher = {World Scientific Publishing Co.},
	author = {Chen, Yifei and Liu, Jihao and Wang, Yanze},
	month = sep,
	year = {2025},
	pages = {2550035},
}