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# Title: Moduli of quiver representations for exceptional collections on surfaces

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 representation 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 many surfaces with such collections.
 Comments: 69 pages, comments are welcome Subjects: Algebraic Geometry (math.AG) Cite as: arXiv:1803.06533 [math.AG] (or arXiv:1803.06533v1 [math.AG] for this version)

## Submission history

From: Xuqiang Qin [view email]
[v1] Sat, 17 Mar 2018 16:26:15 GMT (52kb)