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!

  • $\begingroup$ @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... $\endgroup$ – Eduardo Mar 20 '17 at 20:07
  • $\begingroup$ @Manoel For understanding those theoretical objects, it might be useful to look at a simple and motivating example. $\endgroup$ – reuns Mar 20 '17 at 20:37
  • 1
    $\begingroup$ It is a subvariety of J(R) because it is locally the zero locus of an analytic function: the theta function. $\endgroup$ – Daniele A Mar 21 '17 at 12:07

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