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

Oleksandr Iena, Alain Leytem

Published 2015-11-05Version 1

In the Simpson moduli space $M_{d m-1}(\mathbb P_2)$ of semi-stable sheaves with Hilbert polynomial $dm-1$ on a projective plane we study the closed subvariety 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 $M_{d m-1}(\mathbb P_2)$.