Shokurov's global index conjecture for threefold foliations

TL;DR

This paper proves Shokurov's global index conjecture for three-dimensional foliations, addressing a significant open question in algebraic geometry.

Contribution

It provides a proof of the conjecture specifically for threefold foliations, advancing understanding in the field.

Findings

Confirmed the conjecture for threefold foliations

Answered a question posed by Meng and Xie in dimension three

Utilized generative AI, notably Rethlas, in the research process

Abstract

We prove Shokurov's global index conjecture for foliations in dimension at most three. This answers a question of the first author, Meng, and Xie in dimension three. The main result of this paper is partially obtained by generative AI, particularly the Rethlas system.