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- W2949679413 abstract "Let X be a compact connected Riemann surface of genus at least two and G a connected reductive complex affine algebraic group. The Riemann–Hilbert correspondence produces a biholomorphism between the moduli space $${{mathscr {M}}}_X(G)$$ parametrizing holomorphic G-connections on X and the G-character variety While $${{mathscr {R}}}(G)$$ is known to be affine, we show that $${{mathscr {M}}}_X(G)$$ is not affine. The scheme $${{mathscr {R}}}(G)$$ has an algebraic symplectic form constructed by Goldman. We construct an algebraic symplectic form on $${{mathscr {M}}}_X(G)$$ with the property that the Riemann–Hilbert correspondence pulls back the Goldman symplectic form to it. Therefore, despite the Riemann–Hilbert correspondence being non-algebraic, the pullback of the Goldman symplectic form by the Riemann–Hilbert correspondence nevertheless continues to be algebraic." @default.
- W2949679413 created "2019-06-27" @default.
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- W2949679413 date "2019-05-28" @default.
- W2949679413 modified "2023-10-10" @default.
- W2949679413 title "On the moduli space of holomorphic G-connections on a compact Riemann surface" @default.
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- W2949679413 doi "https://doi.org/10.1007/s40879-019-00345-4" @default.
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