Deformation quantization of moduli spaces of Higgs bundles on a Riemann surface with translation structure

Let X be a compact connected Riemann surface of genus g ≥ 1 equipped with nonzero holomorphic 1-form. MX(r) denote the moduli space semistable Higgs bundles on rank r and degree r(g − 1) + 1; it is complex symplectic manifold. Using translation structure open subset where 1-form does not vanish, we construct natural deformation quantization certain nonempty Zariski MX(r).