Families of G-constellations over resolutions of quotient singularities

2003/05/14 by Timothy Logvinenko, Logvinenko, Timothy · 1 citation
Mathematics · #14J10 #14J17 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras #math.AG #msc:14J10 #msc:14J17

paper · pdf · doi:10.48550/arxiv.math/0305194

39 pages, 9 figures

arxiv created 2003/05/14 · openalex publication_date 2003/05/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite subgroup of GL_n(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.

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