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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.

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    @shaye: I'm just guessing here, since I'm not familiar with this material, but could it be that one of the terms in the equation is not defined for some special configurations of the points?2011-10-02

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