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arXiv · 1511.01847

On the singular sheaves in the fine Simpson moduli spaces of $1$-dimensional sheaves

Oleksandr Iena·Alain Leytem
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Abstract

In the Simpson moduli space $M$ of semi-stable sheaves with Hilbert polynomial $dm-1$ on a projective plane we study the closed subvariety $M'$ of sheaves that are not locally free on their support. We show that for $d\ge 4$ it is a singular subvariety of codimension $2$ in $M$. The blow up of $M$ along $M'$ is interpreted as a (partial) modification of $M\setminus M'$ by vector bundles (on support).

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BibTeXRIS

Oleksandr Iena, Alain Leytem. 2016-05-26. On the singular sheaves in the fine Simpson moduli spaces of $1$-dimensional sheaves. https://arxiv.org/abs/1511.01847

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