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 ∈ H0(End0(E) ⊗ L)) over X of rank r and fixed determinant of degree d. The following conditions are imposed:
(i) deg(L) ≥ 2g−2, r ≥ 2, and L⊗rKX⊗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).