0862１３２人目の素数さん2023/12/27(水) 23:30:48.47ID:Bz9nsHoH>>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
https://mathoverflow.net/questions/142937/motivation-for-multiplier-ideal-sheaves 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. http://www-fourier.ujf-grenoble.fr/~demailly/manuscripts/trieste.pdf 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
15 There's a parallel history of multiplier ideals (especially of the non-dynamic multiplier ideal sheaves on algebraic varieties, say as described in Lazarsfeld's book).
These ideal sheaves are older than Nadel's work. For instance, they were extremely common in the work of Esnault and Viehweg in the early 1980s (see for instance their notes which survey some of this work Lectures on vanishing theorems), also see the works of Kawamata and Kollar. Indeed, these sheaves and slight variants appeared frequently whenever Kawamata-Viehweg vanishing theorems were applied throughout the 1980s. Essentially, the reason why they show up in this context is as follows. You want to prove some Kodaira-type vanishing theorem on a variety that is either non-smooth or with respect to a not-necessarily-ample line bundle. The multiplier ideal lets you correct for this.answered Sep 23, 2013 at Karl Schwede
https://en.wikipedia.org/wiki/Multiplier_ideal Multiplier ideal Multiplier ideals were independently introduced by Nadel (1989) (who worked with sheaves over complex manifolds rather than ideals) and Lipman (1993), who called them adjoint ideals. Multiplier ideals are discussed in the survey articles Blickle & Lazarsfeld (2004), Siu (2005), and Lazarsfeld (2009). (引用終り) 以上
