On a generalized canonical bundle formula and generalized adjunction

TL;DR

This paper extends the canonical bundle formula and adjunction theories to generalized pairs, providing new insights and applications, including progress on a conjecture by Prokhorov and Shokurov.

Contribution

It introduces a generalized framework for canonical bundle formulas and adjunction, advancing the understanding of these concepts in algebraic geometry.

Findings

Extended the canonical bundle formula to generalized pairs

Applied the theory to a case of Prokhorov-Shokurov conjecture

Provided new tools for studying generalized adjunction

Abstract

In this note, we extend the theories of the canonical bundle formula and adjunction to the case of generalized pairs. As an application, we study a particular case of a conjecture by Prokhorov and Shokurov.