  The relation between superholomorphicity and holomorphicity of chiral
superstring N-point amplitudes for NS bosons on a genus 2 Riemann surface is
shown to be encoded in a hybrid cohomology theory, incorporating elements of
both de Rham and Dolbeault cohomologies. A constructive algorithm is provided
which shows that, for arbitrary N and for each fixed even spin structure, the
hybrid cohomology classes of the chiral amplitudes of the N-point function on a
surface of genus 2 always admit a holomorphic representative. Three key
ingredients in the derivation are a classification of all kinematic invariants
for the N-point function, a new type of 3-point Green's function, and a
recursive construction by monodromies of certain sections of vector bundles
over the moduli space of Riemann surfaces, holomorphic in all but exactly one
or two insertion points.
