[過去ﾛｸﾞ] ガロア第一論文と乗数イデアル他関連資料スレ3 (1002ﾚｽ)
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245(2): １３２人目の素数さん [] 2023/04/19(水)21:36 ID:eQ93QFKa(4/6)
>>235
>複素曲面の分脈では
>ブローアップは
>螺旋階段の上下をつなげたようなイメージ
>C^2の原点にリーマン球面を差し込む
下記の”Blowup in a Point”の動画
合ってますか？
上記の説明と合っているように思うのですが・・
https://www.youtube.com/watch?v=20BfjaAZ8sI
Blowup in a Point
oliverlabs
12,334 回視聴 2006/12/08
Today, we present the standard picture which appears in any algebraic geometry text book in the form of an animation: the blowup of the affine plane in the origin. Over each point of the plane there is a unique point in the blowup except for the origin where we have a whole line, called the exceptional line (green). The points on the exceptional line correspond to tangent directions of the affine plane in the origin. Since each lines through the origin passes it in a different direction, the corresponding lines on the blowup do not intersect.
This also allows us to find a smooth curve (blue) on the blowup that lies over the singular blue curve in the plane. The singular point of the plane curve has two preimages since the curve passes through the origin in two different directions (white).
If C is any singular curve lying on a smooth surface it is a classical theorem, that one can find a smooth curve D mapping to C, by iterating this process.
This film was made by Hans-Christian v. Bothmer and Oliver Labs using surfex.
Alok Singh
2 か月前
This is remarkable
fivefoflow
16 年前
Man, I wish I knew what all that stuff in the description means.
246(1): １３２人目の素数さん [] 2023/04/19(水)22:45 ID:j2d9FLUW(3/3)
>>245
合っています
248(1): １３２人目の素数さん [] 2023/04/19(水)23:49 ID:eQ93QFKa(6/6)
>>246
ありがとうございます
なるほど>>245の動画のような図は
昔、森重文先生がフィールズ賞を取ったときの
極小モデル理論解説のポンチ絵で見た記憶が・・
数学セミナー誌だったかな、大衆向けの簡単な説明だったような記憶があります
そうすると、>>245の動画のようなブローアップを
C^2で非可算回続けてブローアップ>>231 するのか・・
分かったような・・、しかし想像を絶する状況ですね
https://ja.wikipedia.org/wiki/%E6%A5%B5%E5%B0%8F%E3%83%A2%E3%83%87%E3%83%AB
極小モデル
https://en.wikipedia.org/wiki/Minimal_model_program
Minimal model program
Minimal models of surfaces
Main article: Enriques?Kodaira classification
Every irreducible complex algebraic curve is birational to a unique smooth projective curve, so the theory for curves is trivial. The case of surfaces was first investigated by the geometers of the Italian school around 1900; the contraction theorem of Guido Castelnuovo（新城） essentially describes the process of constructing a minimal model of any surface.
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