Monad constructions of omalous bundles

We consider a particular class of holomorphic vector bundles relevant for supersymmetric string theory, called \emph{omalous}, over nonsingular projective varieties. We use monads to construct examples of such bundles over 3-fold hypersurfaces in $\mathbb{P}^{4}$, complete intersection Calabi-Yau manifolds in $\mathbb{P}^{k}$, blow-ups of $\mathbb{P}^{2}$ at $n$ distinct points, and products $\mathbb{P}^{m}\times\mathbb{P}^{n}$.