Bulletin of the Korean Mathematical Society (대한수학회보)

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RESOLUTION OF QUOTIENT SINGULARITIES VIA G-CONSTELLATIONS

  • Seung-Jo Jung (Department of Mathematics Education, and Institute of Pure and Applied Mathematics Jeonbuk National University)
  • Received : 2023.04.07
  • Accepted : 2023.07.24
  • Published : 2024.03.31
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Abstract

For a finite subgroup G of GLn(ℂ), the moduli space 𝓜𝜃 of 𝜃-stable G-constellations is rarely smooth. This note shows that for a group G of type ${\frac{1}{r}}(1,a,b)$ with r = abc + a + b, there is a generic stability parameter 𝜃 ∈ Θ such that the birational component Y𝜃 of 𝜃-stable G-constellations provides a resolution of the quotient singularity X := ℂ3/G.

Keywords

Acknowledgement

This work was partially supported by NRF grant (NRF-2021R1C1C1004097) of the Korean government.

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