Here's something that's probably well known to many here, and I'd like to have a suitable reference. I've got a map $f\colon X\to Y$ of complex spaces whose restriction to dense open subspaces $f\colon U\to V$ is the projection of a fibre bundle. Suppose also that $X$ and $Y$ are affine varieties, so that I can consider the fibres of the map $f$ in two different categories. That is, if $p\in V$ is a closed point, I could refine the Zariski topology on the fibre $f^{-1}(p)$ to the complex topology, and the result (I expect) must be homeomorphic to the same fibre in the category of complex spaces. (If true, I could probably learn this much from, say, Shafarevich's *Basic Algebraic Geometry*.)

This leads to my question. Instead of looking at fibres over closed points, I'd probably prefer handling the fibre of $f$ over the generic point of $Y$, which I'll call $f^{-1}(\eta)$. (Does the property that $f$ restricts to a fibre bundle translate to something nice about the variety $f^{-1}(\eta)$?) But I would want to compare the generic fibre, as a topological space, with the typical fibre of $f$ (as a complex space): I'd like to say that, suitably (re)topologized, the two notions of fibre are homeomorphic. However, I don't know how to refine the Zariski topology on the generic fibre, since my base field is now a function field (instead of $\mathbb C$). Does anyone know of some good reading that might sort me out?