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# On the Singular Sheaves in the Fine Simpson Moduli Spaces of $1$-dimensional Sheaves

Published:2016-09-27
Printed: Sep 2017
• Oleksandr Iena,
University of Luxembourg, Campus Kirchberg, Mathematics Research Unit, 6, rue Richard Coudenhove-Kalergi, L-1359 Luxembourg City, Grand Duchy of Luxembourg
• Alain Leytem,
University of Luxembourg, Campus Kirchberg, Mathematics Research Unit, 6, rue Richard Coudenhove-Kalergi, L-1359 Luxembourg City, Grand Duchy of Luxembourg
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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 line bundles (on support).
 Keywords: Simpson moduli spaces, coherent sheaves, vector bundles on curves, singular sheaves
 MSC Classifications: 14D20 - Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13}

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