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

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Abstract

The Hilbert scheme Hilbn C3 of n points on C3\ can be expressed as the critical locus of a regular function on a smooth variety X. Recent development in birational geometry suggests a study of singularities of the pair (X, Hilbn C3) using jet schemes. In this paper, we use a comparison between Hilbn C3 and the scheme C3,n of three commuting n × n matrices to estimate the log canonical threshold of (X, Hilbn C3). As a consequence, we see that although both dimX and dim Hilbn C3 have asymptotic growth O(n2), the largest multiplicity of any points on Hilbn C3 has at most linear growth O(n).

Original languageEnglish
Pages (from-to)397-405
Number of pages9
JournalInternational Journal of Algebra and Computation
Volume34
Issue number3
DOIs
Publication statusPublished - 2024 May 1

All Science Journal Classification (ASJC) codes

  • General Mathematics

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