# multiplicities of rational singularities in higher dimension

For a normal surface rational singularity, we know that the multiplicity of is bounded by $e-1$ where $e$ is the embedding dimension (See for example Miles Reid's book "Chapters on algebraic surfaces").

I am wondering if this inequality also holds in higher dimension. If not, what can we say about the multiplicities.

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Theorem : (C. Huneke and K.-i. Watanabe) The multiplicity of a $d$-dimensional variety with rational singularities and embedding dimension $n$ is at most $${n - 1 \choose d - 1}.$$