Hermitian-Einstein connections on polystable parabolic principal Higgs bundles. (English) Zbl 1258.83007

Summary: Given a smooth complex projective variety \(X\) and a smooth divisor \(D\) on \(X\), we prove the existence of Hermitian-Einstein connections, with respect to a Poincaré-type metric on \(X \setminus D\), on polystable parabolic principal Higgs bundles with parabolic structure over \(D\), satisfying certain conditions on their restriction to \(D\).


83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
53B35 Local differential geometry of Hermitian and Kählerian structures
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