Bounding embedded singularities of Hilbert schemes of points on affine three space

The Hilbert scheme Formula: see text of n points on Formula: see text can be expressed as the critical locus of a regular function on a smooth variety Formula: see text. Recent development in birational geometry suggests a study of singularities of the pair Formula: see text using jet schemes. In this paper, we use a comparison between Formula: see text and the scheme Formula: see text of three commuting Formula: see text matrices to estimate the log canonical threshold of Formula: see text. As a consequence, we see that although both Formula: see text and Formula: see text have asymptotic growth Formula: see text, the largest multiplicity of any points on Formula: see text has at most linear growth Formula: see text.