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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.29 No.1

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A-Hilbert Schemes for 1/r(1^{n-1},a)

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2022, v.29 no.1, pp.59-68
https://doi.org/https://doi.org/10.7468/jksmeb.2022.29.1.59
Jung, Seung-Jo
Jung,, S. (2022). A-Hilbert Schemes for 1/r(1^{n-1},a), 29(1), 59-68, https://doi.org/https://doi.org/10.7468/jksmeb.2022.29.1.59

Abstract

For a finite group G ⊂ GL(n, ℂ), the G-Hilbert scheme is a fine moduli space of G-clusters, which are 0-dimensional G-invariant subschemes Z with H0(𝒪Z ) isomorphic to ℂ[G]. In many cases, the G-Hilbert scheme provides a good resolution of the quotient singularity ℂn/G, but in general it can be very singular. In this note, we prove that for a cyclic group A ⊂ GL(n, ℂ) of type ${\frac{1}{r}}$(1, …, 1, a) with r coprime to a, A-Hilbert Scheme is smooth and irreducible.

keywords
A-Hilbert schemes, cyclic quotient singularities

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics

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