4
$\begingroup$

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!

$\endgroup$
4
$\begingroup$

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

$\endgroup$
  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.