The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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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)
  • Received : 2021.08.04
  • Accepted : 2021.11.29
  • Published : 2022.02.28
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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(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.

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Acknowledgement

I would like to thank the referees for their careful reading.

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