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Bounding embedded singularities of Hilbert schemes of points on affine three space.
- Source :
-
International Journal of Algebra & Computation . May2024, Vol. 34 Issue 3, p397-405. 9p. - Publication Year :
- 2024
-
Abstract
- The Hilbert scheme Hilb n ℂ 3 of n points on ℂ 3 can be expressed as the critical locus of a regular function on a smooth variety . Recent development in birational geometry suggests a study of singularities of the pair (, Hilb n ℂ 3) using jet schemes. In this paper, we use a comparison between Hilb n ℂ 3 and the scheme C 3 , n of three commuting n × n matrices to estimate the log canonical threshold of (, Hilb n ℂ 3). As a consequence, we see that although both dim and dim Hilb n ℂ 3 have asymptotic growth O (n 2) , the largest multiplicity of any points on Hilb n ℂ 3 has at most linear growth O (n). [ABSTRACT FROM AUTHOR]
- Subjects :
- *LOCUS (Mathematics)
*SMOOTHNESS of functions
*GEOMETRY
*MULTIPLICITY (Mathematics)
Subjects
Details
- Language :
- English
- ISSN :
- 02181967
- Volume :
- 34
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- International Journal of Algebra & Computation
- Publication Type :
- Academic Journal
- Accession number :
- 177481361
- Full Text :
- https://doi.org/10.1142/S0218196724500140