The canonical sheaf of Du Bois singularities

2008/01/31 by Sándor J. Kovács, Karl Schwede, Karl E. Schwede +1 · 4 citations
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Polynomial and algebraic computation #math.AC #math.AG #msc:14B05

paper · pdf · doi:10.1016/j.aim.2010.01.020

published as Advances in Mathematics, Volume 224, Issue 4, Pages 1618-1640, 2010 · Minor changes, 21 pages, to appear in Advances in Mathematics

arxiv created 2010/01/30 · openalex publication_date 2010/02/12 · arxiv updated 2010/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a Cohen-Macaulay normal variety X has Du Bois singularities if and only if π_*ω_X'(G) ≃ ω_X for a log resolution π: X' → X, where G is the reduced exceptional divisor of π. Many basic theorems about Du Bois singularities become transparent using this characterization (including the fact that Cohen-Macaulay log canonical singularities are Du Bois). We also give a straightforward and self-contained proof that (generalizations of) semi-log-canonical singularities are Du Bois, in the Cohen-Macaulay case. It also follows that the Kodaira vanishing theorem holds for semi-log-canonical varieties and that Cohen-Macaulay semi-log-canonical singularities are cohomologically insignificant in the sense of Dolgachev.

Citations

• Vanishing and injectivity theorems for LMMP

Cited by

• A short note on Du Bois singularities
• Embeddings of Demi-Normal Varieties
• Centers of perfectoid purity
• Twisted zastava and q-Whittaker functions

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