Is there any well written introduction for the modular space of complex structures on $T^2$?
$\begingroup$
$\endgroup$
3
-
2$\begingroup$ If you mean moduli space, then aren't the complex structures on the 2-torus known and parametrized? (Disclaimer: I am not a geometer, so might be missing something here.) $\endgroup$– Yemon ChoiCommented Aug 30, 2011 at 23:57
-
$\begingroup$ Yes, I know it known, but I need a good reference to understand. I think is upper half plane/ SL(2,Z) action. $\endgroup$– user16750Commented Aug 31, 2011 at 0:04
-
3$\begingroup$ @jc: I think your comment is more appropriate as an answer. There is no obligation to make an answer to a reference request long or deep. $\endgroup$– S. Carnahan ♦Commented Aug 31, 2011 at 2:14
Add a comment
|
2 Answers
$\begingroup$
$\endgroup$
As requested, I'm promoting this comment to an answer:
McKean and Moll's book "Elliptic curves" is a basic introduction to 2-tori with complex structure from the function theoretic, geometric, and arithmetic perspectives. What's closest to what you want is discussed in section 2.6 (on moduli of elliptic curves) and chapter 4 (on the modular group).
$\begingroup$
$\endgroup$
Serre's "A course in arithmetic" is quite nice for this and everything else it covers.