Upper Bound on the Multiplicity of Rational and Du Bois Singularities
Year: 2026
Type: article
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 $\binom{e}{d}$. Additionally, the result recovers the previously known upper bound for the multiplicity of rational singularities.
DOI: 10.1093/imrn/rnag074
Author: Sung Gi Park
Institutions: Princeton University, Institute for Advanced Study
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,534
OpenAlex ID: W7160489676