Semi-toric and toroidal compactifications as log minimal models, and applications to weak K-moduli

Yuji Odaka

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arxiv 2203.09120 v1 pith:RHSQDMKX submitted 2022-03-17 math.AG math.DGmath.NT

Semi-toric and toroidal compactifications as log minimal models, and applications to weak K-moduli

Yuji Odaka This is my paper

classification math.AG math.DGmath.NT

keywords compactificationsk-moduliminimalmodelsrespsemi-torictoroidalweak

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We give a characterization of toroidal (resp., semi-toric) compactifications due to Ash-Mumford-Rapoport-Tai (resp., Looijenga) as log minimal models and apply it to study weak K-moduli compactifications, giving a different proof to a theorem of Alexeev-Engel. We also discuss towards further generalization, in particular revisit Shah-Sterk compactification of moduli of polarized Enriques surfaces to show compatibility with log K-stability.

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For the Eisenstein Deligne-Mostow variety linked to 12 points on P^1, Kirwan's partial resolution is not semi-toroidal, the period map does not lift to the toroidal compactification, the two compactifications are not ...