There is a somewhat loose dictionary between algebro-geometric notions and differential-topological ones. especially if we restrain to the domain of smooth algebraic varieties.
We have notions of a closed embedding of smooth varieties and smooth/etale morphisms of smooth varieties, which might be thought of as counterparts of smooth embeddings and submersions/local diffeomorphisms in the smooth category.
Now is there an analogue of the notion of a map of constant rank, that is such a morphism for which the differential has constant rank at every point?
A nice consequence in differential topology is that then the fibers of this map are smooth submanifolds. In algebraic geometry I am only aware of theorems which assume submersivity to guarantee smooth fibers.
And if there is no such analogues, what is the reason for this difference between smooth and algebraic categories?