Moduli of G-constellations and crepant resolutions I: the abelian case

2022/09/24 by Ryo Yamagishi, Yamagishi, Ryo
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.2209.11900

Abstract

For a finite abelian subgroup G⊂ SL_n(ℂ), we study whether a given crepant resolution X of the quotient variety ℂⁿ/G is obtained as a moduli space of G-constellations. In particular we show that, if X admits a natural G-constellation family in the sense of Logvinenko over it with all fibers being indecomposable as ℂ[ℂⁿ]-modules, then X is isomorphic to the normalization of a fine moduli space of G-constellations.

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