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Log canonical singularities and complete moduli of stable pairs

· 1996 · alg-geom · arXiv alg-geom/9608013

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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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math.AG 1

years

2024 1

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UNVERDICTED 1

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Compactifications of the Eisenstein ancestral Deligne-Mostow variety

math.AG · 2024-03-27 · unverdicted · novelty 6.0

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

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  • Compactifications of the Eisenstein ancestral Deligne-Mostow variety math.AG · 2024-03-27 · unverdicted · none · ref 1 · internal anchor

    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