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861(1): 2023/12/27(水)19:04 ID:TXIc8Mc5(2/2) AAS
multiplier ideal sheafは
Kohnがディーバー方程式の標準解の
境界正則性の問題の研究のために
導入した、PDE由来の概念であるということを
Siuはいつも強調している。

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862: 2023/12/27(水)23:30 ID:Bz9nsHoH(2/3) AAS
>>861
ありがとう
mathoverflowに質問と詳しい回答があるね
・Siu plenary lecture in 2002 icm ”it arose in pde”
・Answer 8 by Nadel a "multiplier ideal sheaf'' But before Nadel , the first person who introduced Multiplier Ideal sheaves was J. Kohn
・あと、Mori、Kawamata、Kodaira-type vanishing theorem が出てきます
・en.wikipediaは、ちょっと雑かな

外部ﾘﾝｸ:mathoverflow.net
motivation for multiplier ideal sheaves asked Sep 23, 2013 Koushik
What is the origin of multiplier ideal sheaves?
It was introduced ny Nadel.Yum Tong Siu,his advisor in his plenary lecture in 2002 icm mentions some thing that it arose in pde.Can anyone kindly elaborate on the motivation behind defining multiplier ideal sheaves.
I think there are lots of experts here in mathoverflow who are experts in these things like diverio and many others.
外部ﾘﾝｸ[pdf]:www-fourier.ujf-grenoble.fr this is I think one of the most standard places to learn about it.

Answer
8
On a Kähler manifold that does not admit Kähler-Einstein metrics there is a nontrivial coherent ideal sheaf, which he called by Nadel a "multiplier ideal sheaf'' But before Nadel , the first person who introduced Multiplier Ideal sheaves was J. Kohn –
user21574 Jul 23, 2017

9
Mori's used a nice method of constructing rational curves in a Fano manifold and later Siu by using study of dynamics of Multiplier ideal sheaves gave a new proof of Mori's theorem, See Siu, Yum-Tong Dynamic multiplier ideal sheaves and the construction of rational curves in Fano manifolds. Complex analysis and digital geometry, 323–360, – user21574 Jul 23, 2017

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