Simple criteria for higher rational singularities

2025/07/10 by Sándor Kovács, Pat Lank, Kovács, Sándor +3 · 1 citation
Computer Science · Mathematics · #13D09 #14A30 #14B05 (primary) #14E15 #32S35 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2507.07351

openalex publication_date 2025/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This work establishes simple criteria for detecting higher rational singularities via the intersection Du Bois complex and the irrationality complex of a normal variety over the complex numbers.

Citations

• Trace for the Du Bois complex
• Complexes of differential forms and singularities: The injectivity theorem
• A short note on Du Bois singularities
• Injectivity and Vanishing for the Du Bois Complexes of Isolated Singularities
• The Holomorphic Extension Property for Higher Du Bois Singularities
• On k-Du Bois and k-rational singularities
• On k-rational and k-Du Bois local complete intersections
• The higher Du Bois and higher rational properties for isolated singularities
• Higher Du Bois and higher rational singularities
• Higher Du Bois singularities of hypersurfaces
• The Du Bois complex of a hypersurface and the minimal exponent
• Hodge theoretic aspects of mirror symmetry

Cited by

• Trace for the Du Bois complex

Related

• Higher Du Bois and higher rational singularities of hypersurfaces
• Upper bound on the multiplicity of rational and Du Bois singularities
• Higher Du Bois and higher rational singularities
• The higher Du Bois and higher rational properties for isolated singularities
• Rational singularities