On a generalized canonical bundle formula and 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.

Improved the exposition. Added Theorem 1.8, which is an alternative version of Theorem 1.7. Added a technical assumption in Theorem 6.7 (previously 6.6)

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