Families of stable bundles of rank 2 with c 1 =−1 on the space ℙ3

Abstract

We construct some infinite series of families of stable rank 2 vector bundles on the projective space ℙ3 with odd first Chern class c1 = −1 and arbitrary second Chern class c2 = 2n with n ≥ 2. They are distinct from the series of families of bundles which were constructed by Hartshorne in 1978. We conjecture that for n ≥ 3 these families lie in the irreducible components of the moduli space of stable bundles distinct from the components that include Hartshorne’s families. In this article we prove the conjecture for n = 3. In this case the scheme of moduli of stable rank 2 vector bundles with c1 = −1 and c2 = 6 on ℙ3 has at least two irreducible components.