Let $X$ be a compact connected Riemann surface of genus $g \geq 1$.
I'm studying a theorem of Faltings which looks as follows.
Let $P_1,\ldots, P_g$ be generic points on $X$. Then we have some equality concerning theta functions. (Details given below in Edit.)
What does it mean that $P_1,\ldots,P_g$ are generic points?
It means that the points don't lie on the theta divisor.