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http://dx.doi.org/10.7468/jksmeb.2022.29.1.59

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

Jung, Seung-Jo (Department of Mathematics Education, Institute of Pure and Applied Mathematics, Jeonbuk National University)
Publication Information
The Pure and Applied Mathematics / v.29, no.1, 2022 , pp. 59-68 More about this Journal
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;
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