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Multiplier Ideals and Modules on Toric Varieties
TLDR
In this article, a simple formula for computing the multiplier ideal of a monomial ideal on an arbitrary affine toric variety is given, and the multiplier module and test ideals are also treated.Abstract:
A simple formula computing the multiplier ideal of a monomial ideal on an arbitrary affine toric variety is given. Variants for the multiplier module and test ideals are also treated.read more
Citations
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Test ideals in non-ℚ-Gorenstein rings
Posted Content
A survey of test ideals
Karl Schwede,Kevin Tucker +1 more
TL;DR: Test ideals were first introduced by Mel Hochster and Craig Huneke in their celebrated theory of tight closure, and since their invention have been closely tied to the theory of Frobenius splittings as mentioned in this paper.
Journal ArticleDOI
The arc space of a toric variety
TL;DR: In this article, the Nash problem on arc families is affirmedatively answered for a toric variety by Ishii and Kollar's paper, which also shows the negative answer for general case.
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F-singularities via alterations
TL;DR: In this article, the authors give characterizations of test ideals and rational singularities via (regular) alterations, and establish Nadel-type vanishing theorems (up to finite maps) for test ideals, and further demonstrate how these vanishing theoresms may be used to extend sections.
References
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Book
Introduction to Toric Varieties.
TL;DR: In this article, a mini-course is presented to develop the foundations of the study of toric varieties, with examples, and describe some of these relations and applications, concluding with Stanley's theorem characterizing the number of simplicies in each dimension in a convex simplicial polytope.
Journal ArticleDOI
The geometry of toric varieties
TL;DR: Affine toric varieties have been studied in this article, where the definition of an affine Toric variety and its properties have been discussed, including cones, lattices, and semigroups.
Book
Tight closure and its applications
TL;DR: The notion of tight closure in equal characteristic zero was introduced by Hochster as mentioned in this paper, who considered the Hilbert-Kunz multiplicity of big Cohen-Macaulay algebras.
Journal ArticleDOI
A generalization of tight closure and multiplier ideals
Nobuo Hara,Ken-ichi Yoshida +1 more
TL;DR: In this article, a new variant of tight closure associated to any fixed ideal a, called α-tight closure, was introduced, and various properties thereof were studied, including the annihilator ideal r(a) of all α tight closure relations.