Shokurov's strong epsilon-lc complement conjecture

From papers

Let (X/PZ,KX+B)(X/P\ni Z,K_X+B) be a dd-dimensional b5b5-lc weak log Fano pair. An (b5,n)(b5,n)-complement over PP (respectively in codimension 22) is an b5b5-lc complement satisfying the stated complement index and coefficient conditions.

Strong b5b5-lc complement conjecture. For every 0<b50<b5 and dd, there exists a finite set a9b5,da9_{b5,d} of positive integers such that every such pair has an (b5,n)(b5,n)-complement over PP (respectively in codimension 22) for some na9b5,dna9_{b5,d}.

This is the stronger uniform boundedness statement for complements, without prescribing a DCC coefficient set. The source relates it to the usual boundedness conjecture for lc complements.

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Sources & referencesView supporting material

Primary source

Caucher Birkar, “Boundedness of ε-log Canonical Complements on Surfaces”, arXiv:math/0409254 (2004).

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