Monad constructions of omalous bundles

TL;DR

This paper constructs examples of omalous holomorphic vector bundles, relevant in string theory, over various complex algebraic varieties using monad techniques, expanding the toolkit for theoretical physics and algebraic geometry.

Contribution

It introduces monad constructions of omalous bundles over diverse algebraic varieties, providing explicit examples in complex geometry and string theory contexts.

Findings

Constructed omalous bundles over 3-fold hypersurfaces in projective space

Developed monad methods for bundles on Calabi-Yau manifolds

Extended constructions to blow-ups and product varieties

Abstract

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 $\mathbb{P}^{m}\times\mathbb{P}^{n}$.