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Regular version of the site

Article

Moduli spaces of rank 2 instanton sheaves on the projective space

Pacific Journal of Mathematics. 2017. Vol. 291. No. 2. P. 399-424.
Jardim M., Maican M., Tikhomirov A. S.

We study the irreducible components of the moduli space of instanton sheaves on P^3, that is, µ-semistable 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) ≤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) = d · 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 T(d) for d ≤ 4.