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

Abstract

We construct a new infinite series of irreducible components of the Gieseker-Maruyama moduli scheme $\mathcal{M}(k), ~ k \geq 3$ of coherent semistable rank 2 sheaves with Chern classes $c_1=0,~ c_2=k,~ c_3=0$ on $\mathbb{P}^3$ 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 union of collections of points and smooth irreducible curves which are rational or complete intersection curves. As a special member of this series we obtain a new component of $\mathcal{M}(3)$.