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642(2): １３２人目の素数さん [] 2023/03/21(火)17:43 ID:8s9PZXQ2(14/20)
>>641
つづき
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
略
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.
It was introduced by Shoshichi Kobayashi in 1967. Kobayashi hyperbolic manifolds are an important class of complex manifolds, defined by the property that the Kobayashi pseudometric is a metric.
https://en.wikipedia.org/wiki/Canonical_singularity
Canonical singularity
https://ja.wikipedia.org/wiki/%E6%A8%99%E6%BA%96%E7%89%B9%E7%95%B0%E7%82%B9
標準特異点
つづく
643(3): １３２人目の素数さん [] 2023/03/21(火)17:43 ID:8s9PZXQ2(15/20)
>>642
つづき
https://en.wikipedia.org/wiki/Commutative_algebra
Commutative algebra
This article is about a branch of algebra. For algebras that are commutative, see Commutative algebra (structure).
Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent examples of commutative rings include polynomial rings; rings of algebraic integers, including the ordinary integers Z ; and p-adic integers.
Commutative algebra is the main technical tool in the local study of schemes.
The study of rings that are not necessarily commutative is known as noncommutative algebra; it includes ring theory, representation theory, and the theory of Banach algebras.
Overview
Commutative algebra is essentially the study of the rings occurring in algebraic number theory and algebraic geometry.
In algebraic number theory, the rings of algebraic integers are Dedekind rings, which constitute therefore an important class of commutative rings.
Connections with algebraic geometry
Commutative algebra (in the form of polynomial rings and their quotients, used in the definition of algebraic varieties) has always been a part of algebraic geometry. However, in the late 1950s, algebraic varieties were subsumed into Alexander Grothendieck's concept of a scheme. Their local objects are affine schemes or prime spectra, which are locally ringed spaces, which form a category that is antiequivalent (dual) to the category of commutative unital rings, extending the duality between the category of affine algebraic varieties over a field k, and the category of finitely generated reduced k-algebras.
つづく
645: １３２人目の素数さん [sage] 2023/03/21(火)17:46 ID:030eOzSs(11/16)
>>641-644
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