“…We first show that genus two n-point correlation functions for n Virasoro vectors are generating functions for the correlation functions for all Virasoro vacuum descendants in a similar fashion to the genus zero and one cases [HT1]. These generating functions satisfy genus two Ward identities (derived from genus two Zhu recursion) which involves genus two generalised Weierstrass functions related to a global (2,1)-bidifferential Ψ(x, y) holomorphic for x = y [GT1]. We also describe some analytic differential equations, which also involve Ψ(x, y), for the genus two bidifferential ω(x, y), normalised holomorphic 1-differentials ν 1 (x), ν 2 (x) and the projective connection s(x).…”