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).