Wall-crossing for iterated Hilbert schemes (or 'Hilb of Hilb')

Autor:	Wormleighton, Ben
Rok vydání:	2021
Předmět:	Mathematics - Algebraic Geometry Mathematics - Representation Theory 14E16 (primary) 14M25 14J17 (secondary)
Druh dokumentu:	Working Paper
Popis:	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 $\theta$-stable representations of the McKay quiver. The stability condition $\theta$ 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. Comment: Written for proceedings of the conference 'The McKay Correspondence, Mutations, and Related Topics' hosted by IPMU in July 2020; 9 pages, 5 figures; comments welcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2112.00079 Zobrazit plný text záznamu View this record from Arxiv