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arXiv · 2111.14718

Smooth Toric Quiver Varieties

Amir Nasr
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Abstract

We study smoothness of toric quiver varieties. When a quiver $Q$ is defined with the identity dimension vector, the corresponding quiver variety is also a toric variety. So it has both fan representation and quiver representation. We work only on quivers with canonical weight and we classify smooth such toric quiver varieties. We show that a variety corresponding to a quiver with the identity dimension vector and the canonical weight is smooth if and only if it is a product of projective spaces or their blowups.

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Amir Nasr. 2021-11-29. Smooth Toric Quiver Varieties. https://arxiv.org/abs/2111.14718

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