2021/11/30 by Wormleighton, Ben
#14E16 (primary) 14M25 #14J17 (secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2112.00079
We study wall-crossing phenomena in the McKay correspondence. Craw-Ishii show that every projective crepant resolution of a Gorenstein abelian quotient singularity arises as a moduli space of θ-stable representations of the McKay quiver. The stability condition θ moves in a vector space with a chamber decomposition in which (some) wall-crossings capture flops between different crepant resolutions. We investigate where chambers for certain resolutions with Hilbert scheme-like moduli interpretations - iterated Hilbert schemes, or 'Hilb of Hilb' - sit relative to the principal chamber defining the usual G-Hilbert scheme. We survey relevant aspects of wall-crossing, pose our main conjecture, prove it for some examples and special cases, and discuss connections to other parts of the McKay correspondence.