Moduli spaces of rank 2 instanton sheaves on the projective space

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 $c_2(E)\le4$, 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 $d\le4$.Comment: 22 page

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Moduli spaces of rank 2 instanton sheaves on the projective space

CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO , FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOWe study the irreducible components of the moduli space of instanton sheaves on P 3 , that is rank 2 torsion free sheaves E with c1(E) = c3(E) = 0 satisfying h 1 (E(−2)) = h 2 (E(−2)) = 0. In particular, we classify all instanton sheaves with c2(E) ≤ 4, describing all the irreducible components of their moduli space. A key ingredient for our argument is the study of the moduli space T (d) of stable sheaves on P 3 with Hilbert polynomial P(t) = dt, which contains, as an open subset, the moduli space of rank 0 instanton sheaves of multiplicity d; we describe all the irreducible components of T (d) for d ≤ 4.2912399424CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO , FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO , FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO303332/2014-0 , 2014/14743-82016/03759-