Abundance theorem for semi log canonical threefolds

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Extension theorems, non-vanishing and the existence of good minimal models (2010, background): “The general strategy for proving that (1.2) implies (1.1) is explained in [Fujino00].”
Log pluricanonical representations and abundance conjecture (2011, unknown): “ishing, abundance, and minimal model conjectures 25 References 27 1. Introduction The followingtheoremis oneofthemainresults ofthispaper(cf.Theorem 3.13). It is a solution of the conjecture raised in [F1] (see [F1, Conjecture 3.2]). For the deﬁnition of the log pluricanonical representation ρm, see ”
Minimal Model Theory for Log Surfaces (2010, unknown): “)| contains no non-klt centers of (X′,∆′). Step 3. If Nlc(X,∆) ∩ Aj = ∅, then OA j (n(KX + ∆)) ≃ OA j for some divisible positive integer n by the abundance theorem for semi log canonical curves (cf. [F1] and [FG, Theorem 1.3]). Anyway, we obtain OA(n(KX + ∆)) ≃ OA for a divisible positive integer n”
Fundamental theorems for semi log canonical pairs (2012, background): “s π-semi-ample. By the arguments in 6.6, we may assume that ∆ is a Q-divisor on X. This reduction seems to be very important because we do not know how to use the gluing arguments for R-divisors (cf. [F3], [FG], [HX]). We note that if ∆ is a Q-divisor then Conjecture 6.7 can be reduced to the case w”
Existence of log canonical closures (2011, background): “[Fujino00] O. Fujino, Abundance theorem for semi log canonical threefolds.”