Log canonical $3$-fold complements

Abstract

We expand the theory of log canonical $3$-fold complements. We prove that if $X\to T$ is a $3$-dimensional contraction of log Calabi-Yau type, then we can find $B\ge 0$ on $X$ for which $(X,B)$ is log canonical and $n(K_X+B){\sim }_{T}0$, where $n$ is an uniform natural number. This means that every $3$-fold of log Calabi-Yau type can be turned into a log Calabi-Yau pair in an effective way.

Improved exposition, comments are welcome

References in corpus (4)

• ACC for minimal log discrepancies of exceptional singularities
• Complements on log canonical Fano varieties
• Q-complements on log surfaces
• Some Results about the Index Conjecture for log Calabi-Yau Pairs

Cited by in corpus (3)

• Boundedness of $(\epsilon ,n)$-Complements for Surfaces
• On singularities of threefold weighted blowups
• Fundamental groups of log Calabi-Yau surfaces