A new series of moduli components of rank-2 semistable sheaves on $\mathbb{P}^{3}$ with singularities of mixed dimension

We construct a new infinite series of irreducible components of the Gieseker-Maruyama moduli scheme $\mathscr{M}(k)$, $k \geq 3$, of semistable rank-2 sheaves on $\mathbb{P}^3$ with Chern classes $c_1=0$, $c_2=k$ and $c_3=0$, whose general points are sheaves with singularities of mixed dimension. These sheaves are constructed by elementary transformations of stable and properly $\mu$-semistable reflexive sheaves along disjoint unions of collections of points and smooth irreducible curves which are rational or complete intersection curves in $\mathbb{P}^{3}$. As a special member of this series, we obtain a new component of $\mathscr{M}(3)$. Bibliography: 12 titles.

rank-2 semistable sheaves, reflexive sheaves, moduli spaces