Let $C_5:=\{{(z_1 \dots, z_5) \in (\mathbb{C})^5 | z_i \neq z_j \forall i\neq j }\}$ be the configuration space of five distinct ordered points in $\mathbb{C}$. Arnold showed that the holomorphic one forms $w_{i,j}:=d log (z_i - z_j)$ satisfy the relation $w_{i,j}\wedge w_{j,k}+ w_{j,k}\wedge w_{k,i}+w_{k,i}\wedge w_{i,j}=0$.This relation is necessary for proving the flatness of KZ connection.

Let $\mathcal{A}_2[2]$ be the space of principally polarized abelian surfaces with level 2 structure. Since $C_5$ parametrizes genus 2 curves with an ordering on their Weirstrass points the Torelli map gives an injection $T:C_5/G \hookrightarrow \mathcal{A}_2[2]$ whose image is the complement of the divisor parametrizing Abelian surfaces which are products of two elliptic curves. Here $G$ is the 2-dimensional group of affine transformations of $\mathbb{C}$.

Is it known which theta functions (perhaps with characteristics) on $\mathcal{A}_2[2]$ pull back to the functions $(z_i -z_j)$ on $C_5$ by the Torelli map $T$? Logarithmic derivative of such theta functions will correspond to the differential forms $w_{i, j}$ on $C_5$ and should satisfy Arnold's relation. Moreover, such an identification will allow to write the KZ connection in terms of logarithmic derivatives of theta functions.

Any comments or references are more than welcome.