Riemann form

• A lattice Λ in a complex vector space C^g.
• An alternating bilinear form α from Λ to the integers satisfying the following Riemann bilinear relations:

1. the real linear extension α_R:C^g × C^g→R of α satisfies α_R=α_R for all in C^g × C^g;
2. the associated hermitian form H=α_R + iα_R is positive-definite.

• The alternatization of the Chern class of any factor of automorphy is a Riemann form.
• Conversely, given any Riemann form, we can construct a factor of automorphy such that the alternatization of its Chern class is the given Riemann form.