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On the Singular Sheaves in the Fine Simpson Moduli Spaces of 1-dimensional Sheaves
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- Journal:
- Canadian Mathematical Bulletin / Volume 60 / Issue 3 / 01 September 2017
- Published online by Cambridge University Press:
- 20 November 2018, pp. 522-535
- Print publication:
- 01 September 2017
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- Article
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In the Simpson moduli space
$M$ of semi-stable sheaves with Hilbert polynomial 
$dm\,\text{-}\,\text{1}$ 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 
$M\backslash {{M}^{'}}$ by line bundles (on support).
