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We construct a canonical compactification of the moduli space of abelian varieties over by adding certain reduced singular varieties along the boundary of , where is a symplectic finite abelian group, is the maximal order of elements of , and is a primitive -th root of unity. In [18] a canonical compactification of was constructed by adding possibly non-reduced GIT-stable (Kempf-stable) degenerate abelian schemes. We prove that there is a canonical bijective finite birational morphism sq : . In particular, the normalizations of and are isomorphic.
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Published: 1 January 2010
First available in Project Euclid: 24 November 2018