Uniform rational polytopes of foliated threefolds and the global ACC

TL;DR

This paper establishes the existence of uniform rational lc polytopes for foliations in dimension three and proves the global ACC for such foliated threefolds, advancing the understanding of their singularities and thresholds.

Contribution

It introduces uniform rational lc polytopes for foliations and proves the global ACC for foliated threefolds with arbitrary DCC coefficients, extending previous results in the field.

Findings

Existence of uniform rational lc polytopes for foliations in dimension ≤ 3

Proof of the global ACC for foliated threefolds with arbitrary DCC coefficients

Analysis of accumulation points of lc thresholds in dimension ≤ 3

Abstract

In this paper, we show the existence of uniform rational lc polytopes for foliations with functional boundaries in dimension $\leq 3$. As an application, we prove the global ACC for foliated threefolds with arbitrary DCC coefficients. We also provide applications on the accumulation points of lc thresholds of foliations in dimension $\leq 3$.