Differential forms on varieties with pre-k-rational singularities

2025/09/04 by Hiatt, Scott
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.04382

Abstract

Let X be a complex algebraic variety. With ℚ-coefficients, the compactly supported cohomology groups Hⁱ_c(X, ℚ) and the compactly supported intersection cohomology groups IHⁱ_c(X, ℚ) have mixed Hodge structures. We compare these two mixed Hodge structures for varieties with pre-k-rational singularities. We then study various notions of differential forms on varieties with pre-k-rational singularities. In particular, we investigate the depth of the complex \underlineΩ^p_X, where \underlineΩ^p_X is the p^th-graded piece of the Du Bois complex.

Citations

• Differential Forms and Hodge Structures on Singular Varieties
• Hodge symmetry and Lefschetz theorems for singular varieties
• Injectivity and Vanishing for the Du Bois Complexes of Isolated Singularities
• Du Bois complexes of cones over singular varieties, local cohomological dimension, and K-groups
• On k-Du Bois and k-rational singularities
• Higher Du Bois and higher rational singularities
• Hodge filtration on local cohomology, Du Bois complex, and local cohomological dimension
• Higher Du Bois singularities of hypersurfaces
• The Du Bois complex of a hypersurface and the minimal exponent
• Mixed Hodge Complexes on Algebraic Varieties

Related

• Differential Forms and Hodge Structures on Singular Varieties
• Low degree Hodge theory for klt varieties
• Higher Du Bois singularities of hypersurfaces
• The intuitive definition of Du Bois singularities
• Higher Du Bois and higher rational singularities