Classification of Monads and a New Moduli Component of Stable Rank 2 Bundles on $$\mathbb {P}^3$$ with Even Determinant and $$c_2=9$$

Abstract The goal of this paper is to classify all minimal monads whose cohomology is a stable rank 2 bundle on $$\mathbb {P}^3$$ P 3 with Chern classes $$c_1=0$$ c 1 = 0 and $$c_2=9$$ c 2 = 9 , with the possible exception of two non-negative minimal monads. This extends the classification of minimal monads given by Hartshorne and Rao in (Hartshorne and Rao 1991, Section 5.3) for $$c_2\le 8$$ c 2 ≤ 8 . We also prove the existence of a new component of the moduli space $$\mathcal {B}(9)$$ B ( 9 ) , which is distinct from the Hartshorne, Ein, and modified Instanton components.