Strong $(\delta ,n)$-complements for semi-stable morphisms

Abstract

We prove boundedness of global strong $(\delta ,n)$-complements for generalized $\epsilon$-log canonical pairs of Fano type. We also prove some partial results towards boundedness of local strong $(\delta ,n)$-complements for semi-stable morphisms. As applications, we prove an effective generalized canonical bundle formula for generalized klt pairs and an effective generalized adjunction formula for exceptional generalized log canonical centers. Moreover, we prove that the existence of strong $(\delta ,n)$-complements implies a conjecture due to M${}^{\mathrm{c}}$Kernan concerning the singularities of the base of a Mori fiber space.

31 pages, final version, to appear in Documenta Mathematica

References in corpus (1)

• Q-complements on log surfaces

Cited by in corpus (2)

• Boundedness of elliptic Calabi-Yau threefolds
• Kawamata log terminal singularities of full rank