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Vortex equation and reflexive sheaves. (English) Zbl 1270.53063
Given a stable holomorphic pair \((E,\phi)\), where \(E\) is a holomorphic vector bundle on a compact Kähler manifold \(X\) and \(\phi\) is a holomorphic section of \(E\), the vector bundle \(E\) admits a Hermitian metric solving the vortex equation. This is generalized to pairs \((\mathcal{E},\phi)\), where \(\mathcal{E}\) is a reflexive sheaf on \(X\), see also [S. B. Bradlow, Commun. Math. Phys. 135, No. 1, 1–17 (1990; Zbl 0717.53075); G. Tian and B. Yang, J. Reine Angew. Math. 553, 17–41 (2002; Zbl 1022.53025)].
MSC:
53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
53B35 Local differential geometry of Hermitian and Kählerian structures
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