Construction of symplectic vector bundles on projective space P3
The moduli spaces of symplectic vector bundles of arbitrary rank on projective space P3 are far from being well-understood. By now the only type of such bundles having satisfactory description are the so-called tame symplectic instantons. It is shown by U. Bruzzo, D. Markushevich and the first author in two papers from 2012 and 2016 that the moduli spaces of tame symplectic instantons are irreducible generically reduced algebraic spaces of dimension prescribed by the deformation theory. In the present paper we construct an infinite series of smooth irreducible moduli components of symplectic vector bundles of an arbitrary even rank 2r , r ≥ 1, obtained by an iterative use of the monad construction applied to tame symplectic instantons. As a particular case we obtain an infinite series of irreducible moduli components of stable rank 2 vector bundles on P3 . We show that this series contains as a subseries a large part of an infinite series of moduli components constructed by the authors and S. Tikhomirov in 2019. We also prove that, for any integers n, r, where r ≥ 1 and n ≥ r + 147, there exists a moduli component, not necessarily unique, of our series such that symplectic bundles from this component have rank 2r and second Chern class n.