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arXiv · 1902.09995

A Kobayashi-Hitchin correspondence between Dirac-type singular mini-holomorphic bundles and HE-monopoles

Masaki Yoshino
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Abstract

We prove an analogue of the Kobayashi-Hitchin correspondence oncompact connected 3-folds that is fibered on orbifold Riemann surfaces and satisfy an integrability condition, which contains compact connected Sasakian 3-folds. We define mini-holomorphic bundles on such 3-folds and the algebraic Dirac-type singularities on mini-holomorphic bundles, and prove that there exists a special Hermitian metric (admissible BHE-metric) on a Dirac-type singular mini-holomorphic bundle if the bundle satisfies a slope stability.

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Masaki Yoshino. 2019-02-26. A Kobayashi-Hitchin correspondence between Dirac-type singular mini-holomorphic bundles and HE-monopoles. https://arxiv.org/abs/1902.09995

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