Recall the definition of Viehweg's variation intimated from *Weak Positivity and the Additivity of the Kodaira Dimension for Certain Fibre Spaces,
E. Viehweg*

Let $f: V\rightarrow W$ be a fiber space (surjective with connected geometric fiber $V_w:=V\times_W \text{Spec }\overline{\mathbb C(W)}$) between two non-singular projective varieties over the field of complex number $\mathbb C$. Then, the variation of $f$, denoted by $\text{Var}(f)$, is defined to be the minimal number $k$, such that there exists a subfield $L$ of $\overline{\mathbb C(W)}$ of transcendental degree $k$ over $\mathbb C$ and a variety $F$ over $k$ with $F\times_{\text{Spec }(L)}\text{Spec }\overline{\mathbb C(W)}$ is birationally equivalent to $V_w$.

Now Let $f: X \rightarrow Y$ be a surjective morphism between smooth projective varieties with connected fibers, and we have a commutative diagram:

such that

- $V$ and $W$ are smooth projective varieties.
- $\alpha$ and $\beta$ are birational.
- All g-exceptional divisors are $\alpha$-exceptional.

**Question**: how to show
$\text{Var}(f)=\text{Var}(g)?$