Let $\pi : X \to T$ be a framed family of elliptic curves (i.e. we have a family of $a(t), b(t) \in H_1(X_t; \mathbb{Z})$ that have $\langle a(t), b(t) \rangle$ in the intersection pairing). One can get a map $\Phi : T \to \mathbb{H}$ (upper half plane) by $\Phi(t) = \int_{a(t)} w_t / \int_{b(t)} w_t$.
Can anyone point me towards a reference where it is proven in detail that $\Phi$ is holomorphic. The notes I'm reading (by Richard Hain - https://arxiv.org/pdf/0812.1803.pdf ) are very sketchy about this - they gave me enough to believe that it is holomorphic, but I want to know how to work with the details.