Moduli of quiver representations for exceptional collections on surfaces

Xuqiang Qin; Shizhuo Zhang

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arXiv · 1803.06533

Moduli of quiver representations for exceptional collections on surfaces

Xuqiang Qin·Shizhuo Zhang

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Abstract

Suppose $S$ is a smooth projective surface over an algebraically closed field $k$, $\mathcal{L}=\{L_1,\ldots,L_n\}$ is a full strong exceptional collection of line bundles on $S$. Let $Q$ be the quiver associated to this collection. One might hope that $S$ is the moduli space of representations of $Q$ with dimension vector $(1,\ldots,1)$ for a suitably chosen stability condition $\theta$: $S\cong M_\theta$. In this paper, we show that this is the case for del Pezzo surfaces. Furthermore, we show the blow-up at a point can be recovered from an augmentation of exceptional collections (in the sense of L. Hille and M.Perling) via morphism between moduli of quiver representations.

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BibTeX RIS

Xuqiang Qin, Shizhuo Zhang. 2018-03-17. Moduli of quiver representations for exceptional collections on surfaces. https://arxiv.org/abs/1803.06533

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