Families of G-constellations over Resolutions of Quotient Singularities

Logvinenko, Timothy ORCID: https://orcid.org/0000-0001-5279-6977 2025. Families of G-constellations over Resolutions of Quotient Singularities. TAIWANESE JOURNAL OF MATHEMATICS 10.11650/tjm/250806

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Abstract

Let G be a finite subgroup of GLn(C). A study is made of the ways in which resolutions of the quotient space Cn/G can parametrise G-constellations, that is, G-regular finite length sheaves. These generalise G-clusters, which are used in the McKay correspondence to construct resolutions of orbifold singularities. A complete classification theorem is achieved, in which all the natural families of G-constellations are shown to correspond to certain finite sets of G-Weil divisors, which are a special sort of rational Weil divisor, introduced in this paper. Moreover, it is shown that the number of equivalence classes of such families is always finite. Explicit examples are computed throughout using toric geometry.

Item Type:	Article
Date Type:	Published Online
Status:	In Press
Schools:	Schools > Mathematics
Publisher:	MATHEMATICAL SOC REP CHINA
ISSN:	1027-5487
Last Modified:	05 Sep 2025 10:30
URI:	https://orca.cardiff.ac.uk/id/eprint/180927

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