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.

16 pages, 1 table

References in corpus (1)

• Two infinite series of moduli spaces of rank 2 sheaves on ${\mathbb{P}}^3$

Cited by in corpus (4)

• Irreducible components of the moduli space of rank 2 sheaves of odd determinant on the projective space
• New series of moduli components of rank 2 semistable sheaves on ${\mathbb{P}}^3$ with singularities of mixed dimension
• A new non-reduced moduli component of rank 2 semistable sheaves on P3
• The spectrum of torsion free sheaves on ${\mathbb{P}}^3$ and applications