The Relative Differential Morphism and the Logarithmic Connection of Dual Conformal Nets

Let $X$ be a compact connected Riemann surface equipped with two nonconstant meromorphic projections $q,z:X\to\mathbb{P}^1$. Their differentials determine a canonical meromorphic relative differential morphism $Z:T_q=q^*T\mathbb{P}^1\to T_z=z^*T\mathbb{P}^1$, whose local coefficient in coordinate fr