Hitchin fibration on moduli of symplectic and orthogonal parabolic Higgs bundles

Abstract

Let $X$ be a compact Riemann surface of genus $g\ge 2$, and let $D\subset X$ be a fixed finite subset. Let $\mathcal{M}(r,d,\alpha )$ denote the moduli space of stable parabolic $G$-bundles (where $G$ is a complex orthogonal or symplectic group) of rank $r$, degree $d$ and weight type $\alpha$ over $X$. Hitchin discovered that the cotangent bundle of the moduli space of stable bundles on an algebraic curve is an algebraically completely integrable system fibered, over a space of invariant polynomials, either by a Jacobian or a Prym variety of spectral curves. In this paper we study the Hitchin fibers for $\mathcal{M}(r,d,\alpha )$.

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• Spectral data for parabolic projective symplectic/orthogonal Higgs bundles