I'm walking towards the Torelli's Theorem.I started from scratch! I did not even know what a divisor was in a Riemann surface. I currently went through Abel's Theorem, theta divisor... Now I am reading the proof of the following theorem:

Theorem 2.25: The theta divisor $\Theta$ of the Jacobian variety $J(R)$, the subvariety $W^{g-1}$ and Riemann's constant are related by following equality:

$\Theta=W^{g-1} + [k]$.

In the reference I'm using https://www.amazon.com/Advances-Moduli-Translations-Mathematical-Monographs/dp/0821821563

After this theorem 2.25 is written: This theorem implies that the polarization of the Jacobian variety is given by the line bundle $[W^{g-1}]$.

I need to read about polarization of the Jacobian variety. Right now I have another very good reference Compact Riemann surfaces (Raghavan Narasimhan), But I did not find out about polarization of the Jacobian variety in this book.

I would like references on the subject. Thank you!


Perhaps http://jmilne.org/math/articles/1986c.pdf helps you. Theorem 6.6 is the principal polarisation of the Jacobian.

  • $\begingroup$ Thank you! Any bibliographic indication on the subjects (theta divisor, jacobian variety, riemann's singularity theorem) Torelli's theorem, is welcome! $\endgroup$ – Manoel Mar 27 '17 at 20:36
  • 2
    $\begingroup$ The Griffiths-Harris might helps. It has a section on Torelli for curves doing the exact steps you need. $\endgroup$ – Enrico Mar 28 '17 at 11:23

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