DHYM connections on higher rank holomorphic vector bundles over $\mathbb{P}(T_{{\mathbb{P}}^2})$

Abstract

We construct the first explicit non-trivial example of deformed Hermitian Yang-Mills (dHYM) connection on a higher rank slope-unstable holomorphic vector bundle over a Fano threefold. Additionally, we provide a sufficient algebraic condition in terms of central charges for the existence of dHYM connections on Whitney sum of holomorphic line bundles over rational homogeneous varieties. As a consequence, we obtain several new examples of dHYM connections on higher rank holomorphic vector bundles.

arXiv commentFinal Version, 23 pages. Comments are welcome. arXiv admin note: substantial text overlap with arXiv:2304.02105

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