Upper bound on the multiplicity of rational and Du Bois singularities

2025/09/26 by Park, Sung Gi · 1 citation
#13H15 #14B05 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.21807

Abstract

This paper resolves a question of Huneke and Watanabe by proving a sharp upper bound for the multiplicity of Du Bois singularities: at a point of a d-dimensional variety with Du Bois singularities and embedding dimension e, the multiplicity is at most \binomed. Additionally, the result recovers the previously known upper bound for the multiplicity of rational singularities.

Citations

• Du Bois complex and extension of forms beyond rational singularities
• On F-pure thresholds
• On the multiplicity of terminal singularities on threefolds
• Subadjunction of log canonical divisors II

Cited by

• The Briançon-Skoda theorem for pseudo-rational and Du Bois singularities and uniformity in excellent rings

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