On moduli spaces of Hitchin pairs

Source abstract

Abstract Let X be a compact Riemann surface X of genus at–least two. Fix a holomorphic line bundle L over X . Let be the moduli space of Hitchin pairs ( E , φ ∈ H 0 (End 0 ( E ) ⊗ L )) over X of rank r and fixed determinant of degree d . The following conditions are imposed: (i) deg( L ) ≥ 2 g −2, r ≥ 2, and L ⊗ r K X ⊗ r ; (ii) ( r, d ) = 1; and (iii) if g = 2 then r ≥ 6, and if g = 3 then r ≥ 4. We prove that that the isomorphism class of the variety uniquely determines the isomorphism class of the Riemann surface X . Moreover, our analysis shows that is irreducible (this result holds without the additional hypothesis on the rank for low genus).