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 derived equivalent, and an automorphic form is constructed on non-hyperelliptic g=4
Log canonical singularities and complete moduli of stable pairs
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abstract
1) Assuming log Minimal Model Conjecture, we give a construction of a complete moduli space of stable log pairs of arbitrary dimension generalizing directly the space M_{g,n} of pointed stable curves. Each stable pair has semi log canonical singularities. 2) We prove that a stable quasiabelian pair, defined by author and I.Nakamura as the limit of abelian varieties with theta divisors, has semi log canonical singularities.
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Complete and optimal characterization of Q-Gorenstein normal affine singularities in terms of K-stability.
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Compactifications of the Eisenstein ancestral Deligne-Mostow variety
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 derived equivalent, and an automorphic form is constructed on non-hyperelliptic g=4