Upper bound on the multiplicity of rational and Du Bois singularities

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 $\left(\genfrac{}{}{0ex}{}{e}{d}\right)$. Additionally, the result recovers the previously known upper bound for the multiplicity of rational singularities.

7 pages; v.2: small expository changes