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857: １３２人目の素数さん [] 2023/02/26(日) 19:55:38.72 ID:ZAlHQVD3

>>856
つづき

https://en.wikipedia.org/wiki/Multiplier_ideal
Multiplier ideal
Algebraic geometry
In algebraic geometry, the multiplier ideal of an effective
Q -divisor measures singularities coming from the fractional parts of D. Multiplier ideals are often applied in tandem with vanishing theorems such as the Kodaira vanishing theorem and the Kawamata?Viehweg vanishing theorem.
Let X be a smooth complex variety and D an effective
Q -divisor on it.
Let μ :X'→ X be a log resolution of D (e.g., Hironaka's resolution).

下記FUJINOより抜粋
P6 5. Resolution Lemma We think that one of the most useful log terminal singularities is divisorial log terminal (dlt, for short), which was introduced by Shokurov (see [FA, (2.13.3)]). We defined it in Definition 4.1 above. By Szab´o’s work [Sz], the notion of dlt coincides with that of weakly Kawamata log terminal (wklt, for short).
P7 By combining Theorem 5.1 with the usual desingularization arguments, we can recover the original Resolution Lemma without any difficulties. This means that, first, we use Hironaka’s desingularization theorem suitably, next, we apply Theorem 5.1 below, then we can recover Szab´o’s results.

つづく

http://rio2016.5ch.net/test/read.cgi/math/1615510393/857

858: １３２人目の素数さん [] 2023/02/26(日) 19:55:59.27 ID:ZAlHQVD3

>>857
つづき

http://www.math.nagoya-u.ac.jp/~fujino/what-HP.pdf
WHAT IS LOG TERMINAL ?
2004/4/23
OSAMU FUJINO
Abstract. In this paper, we explain the subtleties of various
kinds of log terminal singularities. We focus on the notion of
divisorial log terminal singularities, which seems to be the most
useful one. We explain Szab´o’s resolution lemma, the notion of
log resolution, adjunction formula for divisorial log terminal pairs,
and so on. We also collect miscellaneous results and examples on
singularities of pairs in the log MMP that help us understand log
terminal singularities.

Contents
1. What is log terminal? 1
2. Preliminaries on Q-divisors 3
3. Singularities of pairs 5
4. Divisorial log terminal 6
5. Resolution Lemma 6
6. Whitney umbrella 8
7. What is a log resolution? 10
8. Examples 12
9. Adjunction for dlt pairs 14
10. Miscellaneous comments 15
References 16
(引用終り)
以上

http://rio2016.5ch.net/test/read.cgi/math/1615510393/858

861: １３２人目の素数さん [] 2023/02/26(日) 22:37:44.59 ID:ZAlHQVD3

>>859
>乗数イデアル層の解明が進んだこの10年であった

ああ、ありがとう
乗数イデアル層が、重要キーワードなのか
「Siu による乗数イデアルを用いた巧妙な拡張定理の手法 [Si1] 」>>792 藤野
から、下記PDFがヒットしたので貼る

Y.-T. Siu, Invariance of plurigenera, Invent.Math. 134 (1998), no. 3, 661?673.
https://people.math.harvard.edu/~siu/siu_reprints/siu_plurigenera_invent1998.pdf
Invent. math. 134, 661-673 (1998)
DOI 10.1007/s002229800870
Invariance of plurigenera
Yum-Tong Siu*
Department of Mathematics, Harvard University, Cambridge, MA 02138, USA

P2
multiplier ideal sheaf

>>857再録
https://en.wikipedia.org/wiki/Multiplier_ideal
Multiplier ideal
In commutative algebra, the multiplier ideal associated to a sheaf of ideals over a complex variety and a real number c consists (locally) of the functions h such that
|h|^2/Σ|fi^2|^c
is locally integrable, where the fi are a finite set of local generators of the 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).
Algebraic geometry
In algebraic geometry, the multiplier ideal of an effective
Q -divisor measures singularities coming from the fractional parts of D. Multiplier ideals are often applied in tandem with vanishing theorems such as the Kodaira vanishing theorem and the Kawamata?Viehweg vanishing theorem.
Let X be a smooth complex variety and D an effective
Q -divisor on it. Let
μu :X'→ X be a log resolution of D (e.g., Hironaka's resolution).
(引用終り)
以上

http://rio2016.5ch.net/test/read.cgi/math/1615510393/861

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