Take $V$ and $W$ to be projective varieties over $\mathbb{C}$ of dimension $n$ and $m$, respectively. Let $f : V \to W$ be a fibre space, i.e., $f$ is a surjective map whose generic fiber is connected. In a 1983 paper of Viehweg (Weak Positivity and the Additivity of the Kodaira dimension for Certain Fibre Spaces), Viehweg introduces the notion of variation:
Definition: The variation, denoted $\text{var}(f)$, is the smallest number $k$ such that there is a subfield $L$ of $\overline{\mathbb{C}(W)}$ of transcendence degree $k$ over $\mathbb{C}$ and a variety $F$ over $L$ with $F \times_{\text{Spec}(L)} \text{Spec}(\overline{\mathbb{C}(W)})$ birational to the fibre $V_w = f^{-1}(w)$.
Aim: Understand the notion of variation geometrically.