Abelian Differentials

Abstract

The object of this chapter is to explain the meaning of the distinctions involving the relative magnitudes of a, b, and c. The notation here is that of Chapter 1 so the base field is Ω₂ = Q(λ). We define V = V _f to be the Ω₂ space, Lf dx, of differentials of the form ξf dx with ξ ∈ L. We say that ω ∈ V _f is exact if

$$\omega = d\left( {\xi f} \right)$$

(14.0.1)

for some ξ ∈ L.