Complex abelian varieties and Riemann forms
Posted by martin on Wednesday, 30 December 2009 at 21:48
The theory of abelian varieties is very beautiful, both in its arithmetic and geometrical aspects, and also looking just over 
where there are nice applications of complex analysis.
In this post I will work over , and sketch a proof that a complex torus is isomorphic to an abelian variety if and only if it admits a Riemann form.
This will assume some knowledge of the theory of complex manifolds.