Compactification of the moduli space of abelian varieties, Kyoto ...

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8 IKU NAKAMURASimilarlyθ 0 (q, q −3 u)=1+u 3 + q 18 u −3 + q 18 u 6 + ··· ,θ 1 (q, q −3 u)=q −2 u + q 10 u −2 + q 4 u 4 + ··· ,θ 2 (q, q −3 u)=q −2 u 2 + q 4 u −1 + q 10 u 5 + q 28 u −4 + ··· ,lim [θ 0,θ 1 ,θ 2 ](q, q −3 u) = lim [1,q −2 u, u 2 ]=[0, 1, u] in P 2 .q→0 q→0Let w = q −2λ u (a section over a finite extension <strong>of</strong> k(η)) and u ∈ R \ I.(2)lim [θ 0,θ 1 ,θ 2 ](q, q −2λ u)=q→0{[1, 0, 0] (if −1/2
COMPACTIFICATION OF THE MODULI SPACE OF ABELIAN VARIETIES 9By computations we seeD(j + 1 )=[j, j +1]:={x ∈ R; j ≤ x ≤ j +1},2D(λ) ={j} (if j − 1 2
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Compactification of the moduli space of abelian varieties, Kyoto ...

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