Published online by Cambridge University Press: 20 November 2018
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).
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