Abstract

Let X be a connected Riemann surface equipped with a projective structure \(\mathfrak{p}\). Let E be a holomorphic symplectic vector bundle over X equipped with a flat connection. There is a holomorphic symplectic structure on the total space of the pullback of E to the space of all nonzero holomorphic cotangent vectors on X. Using \(\mathfrak{p}\), this symplectic form is quantized. A moduli space of Higgs bundles on a compact Riemann surface has a natural holomorphic symplectic structure. Using \(\mathfrak{p}\), a quantization of this symplectic form over a Zariski open subset of the moduli space of Higgs bundles is constructed.

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