English

Minimal model program for algebraically integrable foliations and generalized pairs

Algebraic Geometry 2026-05-29 v3 Dynamical Systems

Abstract

Using techniques from the theory of foliations, we establish the cone theorem and the contraction theorem for lc generalized pairs in full generality, and meanwhile develop the minimal model program for Q\mathbb Q-factorial foliated dlt algebraically integrable foliations. As an application, we obtain the canonical bundle formula for generalized pairs completely, together with several further consequences, including answering a question of Cascini and Spicer.

Keywords

Cite

@article{arxiv.2309.15823,
  title  = {Minimal model program for algebraically integrable foliations and generalized pairs},
  author = {Guodu Chen and Jingjun Han and Jihao Liu and Lingyao Xie},
  journal= {arXiv preprint arXiv:2309.15823},
  year   = {2026}
}

Comments

The proof of the existence of the flip in V2 has a gap, so we have deleted it (this was also removed from the journal submission version since last year)

R2 v1 2026-06-28T12:34:02.297Z