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A-HILBERT SCHEMES FOR <TEX>${frac{1}{r}}(1^{n-1},;a)$</TEX>
- 한국수학교육학회
- The Pure and Applied Mathematics
- Vol.29 No.1
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2022.0159 - 68 (10 pages)
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DOI : 10.7468/jksmeb.2022.29.1.59
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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 H<sup>0</sup>(𝒪<sub>Z</sub> ) isomorphic to ℂ[G]. In many cases, the G-Hilbert scheme provides a good resolution of the quotient singularity ℂ<sup>n</sup>/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 <TEX>${frac{1}{r}}$</TEX>(1, …, 1, a) with r coprime to a, A-Hilbert Scheme is smooth and irreducible.
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