Singularities on normal varieties

DOI10.1112/S0010437X09003996zbMath1179.14003arXiv0805.1767MaRDI QIDQ3628245

Tommaso de Fernex, Christopher Derek Hacon

Publication date: 19 May 2009

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0805.1767

zbMATH Keywords

multiplier idealssingularities of pairsdivisorial valuationrelative canonical divisor

Mathematics Subject Classification ID

Singularities in algebraic geometry (14B05) Global theory and resolution of singularities (algebro-geometric aspects) (14E15) Singularities of surfaces or higher-dimensional varieties (14J17) Multiplier ideals (14F18)

Related Items (38)

Kähler-Einstein metrics and volume minimization ⋮ Bernstein–Sato functional equations, V-filtrations, and multiplier ideals of direct summands ⋮ Singularities on demi-normal varieties ⋮ Bernstein-Sato Polynomials in Commutative Algebra ⋮ Minimizing normalized volumes of valuations ⋮ On the volume of isolated singularities ⋮ Log terminal singularities ⋮ A transversality theorem for some classical varieties ⋮ Divisorial Models of Normal Varieties ⋮ Deformations of Log Terminal and Semi Log Canonical Singularities ⋮ A characterization of multiplier ideals via ultraproducts ⋮ Resolutions in local algebra and singularity theory. Abstracts from the workshop held February 5--11, 2023 ⋮ Discreteness of 𝐹-jumping numbers at isolated non-ℚ-Gorenstein points ⋮ Discrepancies of non-\(\mathbb Q\)-Gorenstein varieties ⋮ TEST IDEALS IN RINGS WITH FINITELY GENERATED ANTI-CANONICAL ALGEBRAS ⋮ The jumping coefficients of non-\(\mathbb{Q}\)-Gorenstein multiplier ideals ⋮ The volume of an isolated singularity ⋮ Derived invariance of the Albanese relative canonical ring ⋮ Jacobian discrepancies and rational singularities ⋮ Birationally rigid hypersurfaces ⋮ Local volumes of cartier divisors over normal algebraic varieties ⋮ Finitistic test ideals on numerically \(\mathbb{Q}\)-Gorenstein varieties ⋮ Nakamaye's theorem on log canonical pairs ⋮ On the -purity of isolated log canonical singularities ⋮ On isolated singularities with a noninvertible finite endomorphism ⋮ Bernstein -- Sato polynomials on normal toric varieties ⋮ Globally \(F\)-regular and log Fano varieties ⋮ Centers of \(F\)-purity ⋮ Discreteness and rationality of \(F\)-jumping numbers on singular varieties ⋮ Singularities in mixed characteristic via perfectoid big Cohen-Macaulay algebras ⋮ A higher-dimensional generalization of Mumford's rational pullback for Weil divisors ⋮ Test ideals in non-$\mathbb{Q}$-Gorenstein rings ⋮ A note on discreteness of 𝐹-jumping numbers ⋮ Positive characteristic algebraic geometry ⋮ Comparing multiplier ideals to test ideals on numerically ℚ‐Gorenstein varieties ⋮ F-THRESHOLDS OF GRADED RINGS ⋮ Poincaré series of multiplier and test ideals ⋮ Ample Weil divisors

Cites Work

• Dyson's lemma for polynomials in several variables (and the theorem of Roth)
• Multiplier ideal sheaves and Kähler-Einstein metrics of positive scalar curvature
• Rationalité des singularités canoniques
• Invariance of plurigenera
• On Fujita's freeness conjecture for 3-folds and 4-folds
• Multiplier ideals and modules on toric varieties
• Pluricanonical systems on algebraic varieties of general type
• Resolution of singularities of an algebraic variety over a field of characteristic zero. I
• Geometric interpretation of tight closure and test ideals
• The multiplier ideal is a universal test ideal
• Multiplier ideal sheaves and existence of Kähler-Einstein metrics of positive scalar curvature
• Subadjunction of log canonical divisors, II
• Deformations of canonical singularities
• On a generalization of test ideals
• A generalization of tight closure and multiplier ideals
• An interpretation of multiplier ideals via tight closure

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