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Abstract

We present a new family of monads whose cohomology is a stable rank two
vector bundle on $\mathbb{P}^3$. We also study the irreducibility and
smoothness together with a geometrical description of some of these families.
These facts are used to construct a new infinite series of rational moduli
components of stable rank two vector bundles with trivial determinant and
growing second Chern class. We also prove that the moduli space of stable rank
two vector bundles with trivial determinant and second Chern class equal to 5
has exactly three irreducible rational components.