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See detailOn the singular sheaves in the fine Simpson moduli spaces of 1-dimensional sheaves
Iena, Oleksandr UL; Leytem, Alain UL

in Canadian Mathematical Bulletin (2016)

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 ... [more ▼]

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). [less ▲]

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