The Coherent Component of the Moduli of Mckay Quiver Representations for Abelian Groups
نویسنده
چکیده
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 associated G-equivariant k[x1, . . . , xn]-module via Gröbner bases. In the case Mθ = G -Hilb, we show that G -Hilb may be reducible and its coherent component Yθ = Hilb G may be nonnormal, giving examples for G in GL(3, k) and GL(6, k) respectively. The latter answers a question of Nakamura.
منابع مشابه
Moduli of Mckay Quiver Representations I: the Coherent Component
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...
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