Riemann form

In mathematics, a Riemann form in the theory of abelian varieties and modular forms, is the following data: (The hermitian form written here is linear in the first variable.)

Riemann forms are important because of the following: Furthermore, the complex torus Cg/Λ admits the structure of an abelian variety if and only if there exists an alternating bilinear form α such that (Λ,α) is a Riemann form.