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http://dx.doi.org/10.4134/BKMS.b210797

IRREDUCIBILITY OF THE MODULI SPACE FOR THE QUOTIENT SINGULARITY $\frac{1}{2k+1}(k+1,1,2k)$

Seung-Jo, Jung (Department of Mathematics Education, and Institute of Pure and Applied Mathematics Jeonbuk National University)

Publication Information

Bulletin of the Korean Mathematical Society / v.59, no.6, 2022 , pp. 1409-1422 More about this Journal

Abstract

A 3-fold quotient terminal singularity is of the type $\frac{1}{r}(b,1,-1)$ with gcd(r, b) = 1. In [6], it is proved that the economic resolution of a 3-fold terminal quotient singularity is isomorphic to a distinguished component of a moduli space 𝓜_𝜃 of 𝜃-stable G-constellations for a suitable 𝜃. This paper proves that each connected component of the moduli space 𝓜_𝜃 has a torus fixed point and classifies all torus fixed points on 𝓜_𝜃. By product, we show that for $\frac{1}{2k+1}(k+1,1,-1)$ case the moduli space 𝓜_𝜃 is irreducible.

Keywords

Terminal quotient singularities; economic resolutions;

Citations & Related Records

Reference

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