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For moduli of polarized smooth K-trivial a.k.a., Calabi-Yau varieties in ageneral sense, we revisit a classical problem of constructing its "weakK-moduli" compactifications which parametrizes K-semistable (i.e.,semi-log-canonical K-trivial) degenerations. Although weak K-moduli is notunique in general, they always contain a unique partial compactification(K-moduli).  Our main theorem is the log minimality of their normalizations, under someconditions. Partially to confirm that known examples satisfy the conditions, wealso include an appendix on the algebro-geometric reconstruction of Kulikovmodels via the MMP, which has been folklore at least but we somewhatstrengthen.

On log minimality of weak K-moduli compactifications of Calabi-Yau varieties