Singularities on normal varieties

Abstract

In this paper we generalize the definitions of singularities of pairs and multiplier ideal sheaves to pairs on arbitrary normal varieties, without any assumption on the variety being Q-Gorenstein or the pair being log Q-Gorenstein. The main features of the theory extend to this setting in a natural way.

21 pages; v2: final version (minor changes), to appear in Compositio Mathematica

References in corpus (2)

• The canonical sheaf of Du Bois singularities
• Invariants of singularities of pairs

Cited by in corpus (32)

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• Discreteness and rationality of $F$-jumping numbers on singular varieties
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• Singularities in mixed characteristic via perfectoid big Cohen-Macaulay algebras
• Kähler-Einstein metrics and volume minimization
• Test ideals in rings with finitely generated anti-canonical algebras
• Loop structure on equivariant $K$-theory of semi-infinite flag manifolds
• Singularities with respect to Mather-Jacobian discrepancies
• On the Volume of Isolated Singularities
• Minimizing normalized volumes of valuations
• Discrepancies of non-$\Q$-Gorenstein varieties
• Local volumes on normal algebraic varieties
• Twisted zastava and $q$-Whittaker functions
• Comparing multiplier ideals to test ideals on numerically Q-Gorenstein varieties
• Integrally Closed Ideals on Log Terminal Surfaces are Multiplier Ideals
• Embeddings of Demi-Normal Varieties
• Arithmetic and geometric deformations of $F$-pure and $F$-regular singularities
• Reductive quotients of klt singularities
• On Semirational Singularities
• About a Minimal Model Program without flips
• The jumping coefficients of non-Q-Gorenstein multiplier ideals
• A Gorenstein criterion for strongly $F$-regular and log terminal singularities
• Holomorphic self-maps of singular rational surfaces
• Towards a link theoretic characterization of smoothness
• A Transversality Theorem for some Classical Varieties
• Ample Weil divisors
• Some properties and examples of log terminal+ singularities
• A class of singularity of arbitrary pairs and log canonicalizations
• Discreteness of $F$-jumping numbers at isolated non-Q-Gorenstein points
• Rational and Semi-Rational Singularities