On Moduli Space of Higgs GO(m,ℂ) Bundles Over a Riemann Surface

Let X be a compact connected Riemann surface; the holomorphic cotangent bundle of X will be denoted by K_X. Let M_H denote the moduli space of semi-stable Higgs GO(m,ℂ)-bundles over X of fixed topological type. The complex variety M_H has a natural holomorphic symplectic structure. On the other hand, for any d₀≥1, the Liouville symplectic form on the total space of K_X defines a holomorphic symplectic structure on the Hilbert scheme Hilb^d₀ (K_X) parametrizing the 0-dimensional subschemes of K_X. We relate the symplectic form on Hilb^d₀ (K_X) with the symplectic form on M_H.