English

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

Algebraic Geometry 2025-11-26 v2 Differential Geometry

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.

Keywords

Cite

@article{arxiv.2307.05787,
  title  = {DHYM connections on higher rank holomorphic vector bundles over ${\mathbb{P}}(T_{{\mathbb{P}^{2}}})$},
  author = {Eder M. Correa},
  journal= {arXiv preprint arXiv:2307.05787},
  year   = {2025}
}

Comments

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