Log canonical singularities and complete moduli of stable pairs

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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References in corpus (3)

• Quotients by Groupoids
• Quotient Spaces Modulo Algebraic Groups
• On Mumford's construction of degenerating abelian varieties

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