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

Jung, Seung-Jo; Jung, Seung-Jo

doi:https://doi.org/10.7468/jksmeb.2022.29.1.59

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P-ISSN3059-0604
E-ISSN3059-1309
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ISSN : 3059-0604

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Vol.29 No.1

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A-HILBERT SCHEMES FOR ${\frac{1}{r}}(1^{n-1},\;a)$

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

한국수학교육학회지시리즈B:순수및응용수학 / 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 (Department of Mathematics Education, Institute of Pure and Applied Mathematics, Jeonbuk National University)

Jung, Seung-Jo. (2022). A-HILBERT SCHEMES FOR <TEX>${\frac{1}{r}}(1^{n-1},\;a)$</TEX>, 29(1), 59-68, https://doi.org/https://doi.org/10.7468/jksmeb.2022.29.1.59

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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(𝒪_Z ) 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

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논문 상세

Vol.29 No.1

A-HILBERT SCHEMES FOR ${\frac{1}{r}}(1^{n-1},\;a)$

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

Abstract

한국수학교육학회지시리즈B:순수및응용수학