VOL. 88 | 2023 Invariant Hilbert scheme of the Cox realization of the nilpotent cone in $\mathfrak{sl}(n)$
Ayako Kubota

Editor(s) Yukari Ito, Akira Ishii, Osamu Iyama

Adv. Stud. Pure Math., 2023: 517-533 (2023) DOI: 10.2969/aspm/08810517

Abstract

We pose a question asking if the main component of the invariant Hilbert scheme of the Cox realization of a given singularity is a resolution of singularities. As a concrete example, we consider the case where the singularity is the nilpotent cone in $\mathfrak{sl}(n)$, and we see that in this case the answer to the question is positive.

Information

Published: 1 January 2023
First available in Project Euclid: 8 May 2023

Digital Object Identifier: 10.2969/aspm/08810517

Subjects:
Primary: 17B08
Secondary: 14B05 , 14E16

Keywords: the Cox ring , the invariant Hilbert scheme

Rights: Copyright © 2023 Mathematical Society of Japan

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