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⊗r
KX⊗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
![](//static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20151023085953106-0027:S0305004111000405_char1.gif?pub-status=live)
uniquely determines the isomorphism class of the Riemann surface
X. Moreover, our analysis shows that
![](//static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20151023085953106-0027:S0305004111000405_char1.gif?pub-status=live)
is irreducible (this result holds without the additional hypothesis on the rank for low genus).