Construction of Stable Rank 2 Bundles on ℙ3 Via Symplectic Bundles

• Published in: Siberian mathematical journal Vol. 60; no. 2; pp. 343 - 358
• Main Authors: Tikhomirov, A. S., Tikhomirov, S. A., Vassiliev, D. A.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 2019; Springer Nature B.V
• Subjects: Bundles; Bundling; Homology; Infinite series; Mathematics; Mathematics and Statistics; Sheaves; moduli of stable bundles; rank 2 bundles; symplectic bundles
• ISSN: 0037-4466; 1573-9260
• DOI: 10.1134/S0037446619020150

In this article we study the Gieseker–Maruyama moduli spaces ℬ ( e, n ) of stable rank 2 algebraic vector bundles with Chern classes c 1 = e ∈ {−1, 0} and c 2 = n ≥ 1 on the projective space ℙ 3 . We construct the two new infinite series Σ 0 and Σ 1 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 Σ 0 contains components for all big enough values of n (more precisely, at least for n ≥ 146). Σ 0 yields the next example, after the series of instanton components, of an infinite series of components of ℬ (0, n ) satisfying this property.