On the B-Semiampleness Conjecture

TL;DR

This paper advances the understanding of the B-Semiampleness Conjecture by proving semi-ampleness of the moduli part on high divisorial valuations under certain assumptions, contributing to the minimal model program.

Contribution

It proves semi-ampleness of the moduli part on high divisorial valuations assuming the conjecture holds in lower dimensions, advancing the conjecture's partial validation.

Findings

Semi-ampleness of the moduli part on high divisorial valuations.

Conditional proof based on lower-dimensional cases.

Progress towards the B-Semiampleness Conjecture.

Abstract

The B-Semiampleness Conjecture of Prokhorov and Shokurov predicts that the moduli part in a canonical bundle formula is semiample on a birational modification. We prove that the restriction of the moduli part to any sufficiently high divisorial valuation is semiample, assuming the conjecture in lower dimensions.