Moduli spaces of rank 2 instanton sheaves on the projective space

Abstract

We study the irreducible components of the moduli space of instanton sheaves on ${\mathbb{P}}^3$, that is rank 2 torsion free sheaves $E$ with $c_1(E)=c_3(E)=0$ satisfying $h^1(E(-2))=h^2(E(-2))=0$. In particular, we classify all instanton sheaves with $c_2(E)\le 4$, describing all the irreducible components of their moduli space. A key ingredient for our argument is the study of the moduli space $\mathcal{T}(d)$ of stable sheaves on ${\mathbb{P}}^3$ with Hilbert polynomial $P(t)=d\cdot t$, which contains, as an open subset, the moduli space of rank 0 instanton sheaves of multiplicity $d$; we describe all the irreducible components of $\mathcal{T}(d)$ for $d\le 4$.

22 pages

References in corpus (1)

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

Cited by in corpus (4)

• Instantons: the next frontier
• Instanton sheaves and representations of quivers
• On the fixed locus of framed instanton sheaves on ${\mathbb{P}}^3$
• Monads on projective varieties