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NCTS Seminar on Algebraic Geometry
16:00 - 17:00, June 1, 2018 (Friday)
Room 440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
G-constellations and the Maximal Resolution of a Quotient Surface Singularity
Akira Ishii (Nagoya University)


For a finite subgroup G of GL(2,C), it is known that the Hilbert scheme G-Hilb(C^2), which parameterizes “G-clusters”, is the minimal resolution of the quotient singularity. Generalizing it, we consider the moduli space of “G-constellations”, which are certain G-equivariant coherent sheaves. The moduli space depends on the choice of a stability parameter. For a generic stability parameter, it is a resolution of the quotient singularity and its derived category can be embedded into that of the quotient stack. The problem we address is to characterize these moduli spaces among resolutions of the quotient singularity.


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