Effective log canonical boundary conjecture for normal quasi-projective qlc pairs

Let [X,ω][X,\omega] be a qlc pair, where XX is a quasi-projective normal scheme. An effective Q\mathbb Q-divisor on XX is a divisor Δ0\Delta\geq 0 with rational coefficients. A pair (X,Δ)(X,\Delta) is log canonical when it has log canonical singularities.

Effective log canonical boundary conjecture. There exists an effective Q\mathbb Q-divisor Δ\Delta on XX such that (X,Δ)(X,\Delta) is log canonical.

This is posed as a conjecture for normal qlc pairs. It asks whether every quasi-projective normal qlc pair admits an effective boundary making the underlying pair log canonical; the supplied source does not state a resolution.

Sources & referencesView supporting material

Primary source

Osamu Fujino and Haidong Liu, “On normalization of quasi-log canonical pairs”, arXiv:1711.10060 (2018).

Additional references

2 papers in this index state this conjecture (2015–2017). The statement above is taken from the most recent of them; the others are arXiv:1509.07268.

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.