Moduli of Mckay Quiver Representations I: the Coherent Component
نویسندگان
چکیده
For a finite abelian group G ⊂ GL(n, k), we describe the coherent component Yθ of the moduli space Mθ of θ-stable McKay quiver representations. This is a not-necessarily-normal toric variety that admits a projective birational morphism Yθ → Ak /G obtained by variation of GIT quotient. As a special case, this gives a new construction of Nakamura’s G-Hilbert scheme Hilb that avoids the (typically highly singular) Hilbert scheme of |G|-points in A k . To conclude, we describe the toric fan of Yθ and hence calculate the quiver representation corresponding to any point of Yθ.
منابع مشابه
The Coherent Component of the Moduli of Mckay Quiver Representations for Abelian Groups
For a finite abelian group G ⊂ GL(n, k), we describe the coherent component Yθ of the moduli space Mθ of McKay quiver representations. This is a not-necessarily-normal toric variety that admits a projective birational morphism Yθ → A/G obtained by variation of GIT quotient. We present a simple calculation to determine the quiver representation corresponding to any point of Yθ, and describe the ...
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