Minimal model program for algebraically integrable adjoint foliated structures

TL;DR

This paper develops a minimal model program for algebraically integrable adjoint foliated structures, establishing key theorems like the cone and contraction theorems, and proving the existence of flips and minimal models.

Contribution

It introduces the minimal model program for these structures, including the cone theorem, contraction theorem, flips, and base-point-freeness, advancing the understanding of foliated algebraic geometry.

Findings

Proved the cone theorem for algebraically integrable adjoint foliated structures.

Established the existence of flips and minimal models.

Proved the base-point-freeness theorem for structures of general type.

Abstract

For $\mathbb Q$-factorial klt algebraically integrable adjoint foliated structures, we prove the cone theorem, the contraction theorem, and the existence of flips. Therefore, we deduce the existence of the minimal model program for such structures. We also prove the base-point-freeness theorem for such structures of general type and establish an adjunction formula and the existence of $\mathbb Q$-factorial quasi-dlt modifications for algebraically integrable adjoint foliated structures.