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arXiv · 1810.04737

Compactification of the moduli space of instanton sheaves on the Fano threefold $V_5$

Xuqiang Qin
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Abstract

We study semistable sheaves of rank $2$ with Chern classes $c_1=0$, $c_2=2$ and $c_3=0$ on the Fano 3-fold $V_5$ of Picard number $1$, degree $5$ and index $2$. We show that the moduli space of such sheaves has a component that is isomorphic to $\mathbb{P}^5$ by identifying it with the moduli space of semistable quiver representations. This provides a natural smooth compactification of the moduli space of minimal instantons, as well as Ulrich bundles of rank $2$ on $V_5$.

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Xuqiang Qin. 2018-10-10. Compactification of the moduli space of instanton sheaves on the Fano threefold $V_5$. https://doi.org/10.1016/j.jpaa.2020.106526

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