pith. sign in

arxiv: 2309.15823 · v3 · pith:HGR526X5new · submitted 2023-09-27 · 🧮 math.AG · math.DS

Minimal model program for algebraically integrable foliations and generalized pairs

classification 🧮 math.AG math.DS
keywords foliationsgeneralizedpairsalgebraicallyintegrableminimalmodelprogram
0
0 comments X
read the original 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 $\mathbb Q$-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.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Shokurov's global index conjecture for threefold foliations

    math.AG 2026-05 unverdicted novelty 7.0

    Proves Shokurov's global index conjecture for foliations on varieties of dimension at most three.

  2. Optimal bend-and-break for foliations

    math.AG 2026-05 unverdicted novelty 6.0

    The optimal constant in the bend-and-break inequality for foliations of rank r on normal projective varieties is r+1.

  3. Birational boundedness of stable families

    math.AG 2026-04 unverdicted novelty 6.0

    Algebraically integrable foliations of fixed dimension and bounded adjoint volume are log birationally bounded, which implies birational boundedness for stable families of maximal variation.

  4. Optimal bend-and-break for foliations

    math.AG 2026-05 unverdicted novelty 5.0

    For every foliation of rank r on a normal projective variety, the optimal constant in the bend-and-break inequality for tangent rational curves is r+1.