2 problems

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Effective log canonical boundary conjecture for normal quasi-projective qlc pairs
Effective log canonical boundary conjecture. There exists an effective $mathbb Q$ -divisor $Delta$ on $X$ such that $(X,\Delta)$ is log canonical.
Conjectureopenlog-canonical-pairs quasi-log-canonicalarXiv posted 2 days ago
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Fujino's simple connectedness conjecture for projective quasi-log canonical pairs
Fujino's simple connectedness conjecture. $X$ is simply connected.
Conjectureopenfano-varieties fundamental-groups quasi-log-canonicalarXiv posted 2 days ago

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