Hodge theory meets the minimal model program: a survey of log canonical and Du Bois singularities

Abstract

This is a survey of some recent developments in the study of singularities related to the classification theory of algebraic varieties. In particular, the definition and basic properties of Du Bois singularities and their connections to the more commonly known singularities of the minimal model program are reviewed and discussed.

35 pages. To appear in the Proceedings of the MSRI Workshop on the Topology of Stratified Spaces

References in corpus (3)

• Semi log resolution
• Two examples of surfaces with normal crossing singularities
• Hulls and Husks

Cited by in corpus (16)

• Differential Forms on Log Canonical Spaces
• A survey of test ideals
• Supplements to non-lc ideal sheaves
• Rational cohomology tori
• Inversion of adjunction for rational and Du Bois pairs
• The weak ordinarity conjecture and $F$-singularities
• Differential forms on singular spaces, the minimal model program, and hyperbolicity of moduli stacks
• The Angehrn-Siu Type Effective Freeness For Quasi-Log Canonical Pairs
• Singularities of stable varieties
• Regularity, singularities and $h$-vector of graded algebras
• F-injectivity and Buchsbaum singularities
• The dualizing complex of $F$-injective and Du Bois singularities
• D-modules in birational geometry
• On isolated log canonical centers
• K-theoretic defect in Chern class identity for a free divisor
• Steenbrink vanishing extended