  We compute equations for real multiplication on the divisor classes of genus
two curves via algebraic correspondences. We do so by implementing van
Wamelen's method for computing equations for endomorphisms of Jacobians on
examples drawn from the algebraic models for Hilbert modular surfaces computed
by Elkies and Kumar. We also compute a correspondence over the universal family
for the Hilbert modular surface of discriminant 5 and use our equations to
prove a conjecture of A. Wright on dynamics over the moduli space of Riemann
surfaces.
