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Step3.
There exists a positive number p depending only on d, eps, n, Q such that we can find a very ample divisor H ≥ 0 on V with pAv - H being big.
---- Step2 的落点是 Av = ψ*Aw. (W 已替换).
---- 此处是在 V 空间里办事情.
---- 用“条件方程” 产生新空间和新参数: pAv - H ~ big.
---- 做出 H 该是要套用Th1.6( ≤d).
(征兆是 very ample divisor H).
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Then Hᵈ⁻¹·(ψ*φ*Ω)
.....= (ψ*H)ᵈ⁻¹·φ*Ω
.....≤ (ψ*H +φ*Ω)ᵈ
.....= vol(ψ*H + φ*Ω)
.....≤ vol(pAw + φ*Ω)
.....≤ vol(pA + Ω)
.....≤ vol(-(pn + 1)Kx) ...
---- 给出了一通估计 (Ω 显示出贯穿性).
---- 怎么想到的 ?
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... which implies the left hand side intersection number is bounded from above, hence the coefficients of ψ*φ*Ω are bounded from above depending only on d, eps, n, Q.
---- 意味着左端的 截交数 有上界, 因此 ψ*φ*Ω 的系数有上界 (只依赖于 d, eps, n, Q).
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评论:出现较新的推导, 且容推敲。
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小结: Step3 就这么两句话 .