Stability of degenerate abelian varieties

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,1/N] by introducing the noncommutative level structures. Any degenerate abelian scheme on the boundary of the compactification is a singular one among our models – projectively stable quasi-abelian schemes. We prove that a degenerate abelian scheme has Kempf-stable Hilbert points if and only if it is a projectively stable quasi-abelian scheme.