Injectivity and Vanishing for the Du Bois Complexes of Isolated Singularities

2024/09/26 by Popa, Mihnea, Shen, Wanchun, Vo, Anh Duc · 6 citations
#14B05 #14F17 #32S35 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.18019

Abstract

We prove an injectivity theorem for the cohomology of the Du Bois complexes of varieties with isolated singularities. We use this to deduce vanishing statements for the cohomologies of higher Du Bois complexes of such varieties. Besides some extensions and conjectures in the non-isolated case, we also provide analogues for intersection complexes.

Cited by

• Higher Du Bois and Higher Rational Pairs
• Inversion of adjunction for higher rational singularities
• Differential forms on varieties with pre-k-rational singularities
• Unobstructed deformations for singular Calabi-Yau varieties
• Trace for the Du Bois complex
• Simple criteria for higher rational singularities

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• On k-Du Bois and k-rational singularities
• The intuitive definition of Du Bois singularities
• Du Bois complexes of cones over singular varieties, local cohomological dimension, and K-groups
• Generic Vanishing for Singular Varieties via Du Bois complexes