A Vanishing Result for the Universal Bundle on a Toric Quiver Variety

Details A Vanishing Result for the Universal Bundle on a Toric Quiver Variety A Vanishing Result for the Universal Bundle on a Toric Quiver Variety

1997-06-23

arxiv.org/abs/alg-geom/9706008v1

Mathematics

Algebraic Geometry

13 pages with a couple of small figures LaTeX 2.09

Scientific paper

Let Q be a finite quiver without oriented cycles. Denote by U --> M the fine moduli space of stable thin sincere representations of Q with respect to the canonical stability notion. We prove Ext^i(U,U) = 0 for all i >0 and compute the endomorphism algebra of the universal bundle U. Moreover, we obtain a necessary and sufficient condition for when this algebra is isomorphic to the path algebra kQ of the quiver Q. If so, then the bounded derived category of finitely generated right kQ-modules is embedded into that of coherent sheaves on M.

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