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arXiv · 2403.15719

Harmonic Bundles with Symplectic Structures

Takashi Ono
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Abstract

We study harmonic bundles with an additional structure called symplectic structure. We study them for the case of the base manifold is compact and non-compact. For the compact case, we show that a harmonic bundle with a symplectic structure is equivalent to principle $Sp(2n,C)$-bundle with a reductive flat connection. For the non-compact case, we show that a polystable good filtered Higgs bundle with a perfect skew-symmetric pairing is equivalent to a good wild harmonic bundle with a symplectic structure.

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Takashi Ono. 2024-03-23. Harmonic Bundles with Symplectic Structures. https://arxiv.org/abs/2403.15719

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