Proves an upper limit on the multiplicity of Du Bois singularities, suggesting implications for rational singularities.
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 ed. Additionally, the result recovers the previously known upper bound for the multiplicity of rational singularities.
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Sung Gi Park (2026) studied this question.
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