Title: Semistable rank 2 sheaves with singularities of mixed dimension on $\mathbb{P}^3$,
Abstract: We describe new irreducible components of the Gieseker-Maruyama moduli scheme
$\mathcal{M}(3)$ of semistable rank 2 coherent sheaves with Chern classes
$c_1=0,\ c_2=3,\ c_3=0$ on $\mathbb{P}^3$, general points of which correspond
to sheaves whose singular loci contain components of dimensions both 0 and 1.
These sheaves are produced by elementary transformations of stable reflexive
rank 2 sheaves with $c_1=0,\ c_2=2,\ c_3=2$ or 4 along a disjoint union of a
projective line and a collection of points in $\mathbb{P}^3$. The constructed
families of sheaves provide first examples of irreducible components of the
Gieseker-Maruyama moduli scheme such that their general sheaves have
singularities of mixed dimension.