# Jacobian variety, theta divisor

I'm reading about Jacobian Varieties... So I find the definition of theta divisor

$\Theta=\{[z] \in J(R)| \theta(\tau,z)=0\}$, where $\theta(\tau,z)$ is the theta funcion. Then the author writes:"The subvariety $\Theta$ is called a theta divisor."

My question is: why $\Theta$ is a subvariety? subvariety of $J(R)$? Any help is welcome, including bibliography. It's a new subject for me.

thank you!

• @Manoel Could you start explaining who is $J(R)$ and who is the theta function $\theta$, maybe in some particular case, or even in which book are you studing... – Eduardo Mar 20 '17 at 20:07
• @Manoel For understanding those theoretical objects, it might be useful to look at a simple and motivating example. – reuns Mar 20 '17 at 20:37
• It is a subvariety of J(R) because it is locally the zero locus of an analytic function: the theta function. – Daniele A Mar 21 '17 at 12:07