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从陌生到熟悉~
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This is an in-mail from TYUST.
本期开始分组发送邮件，搭载数学类学院等链接。
从陌生到熟悉~
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Replacing X with a Q-factorialisation, we can assume X is Q-factorial.
---- 用 Q-因式化对 X 做替换, 可假设 X 是 Q-factorial.
---- 做该替换的理由是什么?
---- 与其做替换, 为何不直接作为条件?
(肯定有某种道理..暂时当作方法接受).
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There is a prime divisor T over X, that is, on birational models of X, with log discrepancy a(T, X, B + sL) = eps'.
There is a prime divisor T over X, that is, on birational models of X, with log discrepancy a(T, X, B + sL) = eps'.
---- 存在 T 使得 a(T, X, B + sL) = eps'.
---- a(T, ...) = eps' 简称 “eps-通”.
---- 若用 0 替换 eps', 则称作“通”.
(此处的名称只是为了方便指代)
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If T is not exceptional over X, then we let φ: Y --> X be the identity morphism.
---- 若 T 非超越, 则令φ: Y --> X 为恒等态射.
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But if T is exceptional over X, then we let φ: Y --> X be the extremal birational contraction which extracts T.
---- 若 T 是超越的, 则令φ: Y --> X 为 极双有理压缩 (ebc), 它提取 T.
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Let KY + BY = φ*(Kx + B) and let LY = φ*L.
---- (转到Y空间)
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By assumption, μTBY ≤ 1 - eps but μT(BY + sLY) = 1 - eps', hence μTsLY ≥ eps - eps'.
---- 前半句待考.(?)
---- hence 后的结果是通过简单代入得到.
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评论: 第一段的落点是 μTsLY ≥ eps - eps' (意义待考 ?).
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小结: 第一段出现的式子都很典型.
https://blog.sciencenet.cn/blog-315774-1190515.html
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