# ag.algebraic geometry – A question on effective divisors

Let $$X$$ be a projective variety with two morphisms $$f:Xrightarrow Y$$ and $$g:Xrightarrow Z$$. Assume that $$Pic(X) = f^{*}Pic(Y)oplus g^{*}Pic(Z)$$. Then if $$D$$ is a divisor on $$X$$ we can write $$D = f^{*}D_Y + g^{*}D_Z$$, where $$D_Y,D_Z$$ are divisors on $$Y$$ and $$Z$$ respectively.

If $$D$$ is effective are then $$D_Y$$ and $$D_Z$$ effective as well?

This holds for instance when $$X = mathbb{P}^n times mathbb{P}^m$$ is a product and $$f,g$$ are the projections onto the factors.