Construction of Stable Rank 2 Bundles on ℙ3 Via Symplectic Bundles

Abstract

In this article we study the Gieseker–Maruyama moduli spaces ℬ(e, n) of stable rank 2 algebraic vector bundles with Chern classes c₁ = e ∈ {−1, 0} and c₂ = n ≥ 1 on the projective space ℙ³. We construct the two new infinite series Σ₀ and Σ₁ of irreducible components of the spaces ℬ(e, n) for e = 0 and e = −1, respectively. General bundles of these components are obtained as cohomology sheaves of monads whose middle term is a rank 4 symplectic instanton bundle in case e = 0, respectively, twisted symplectic bundle in case e = −1. We show that the series Σ₀ contains components for all big enough values of n (more precisely, at least for n ≥ 146). Σ₀ yields the next example, after the series of instanton components, of an infinite series of components of ℬ(0, n) satisfying this property.