# Complex geometry – Fiber identical to the induced coverage map

Consider a holomorphic map $$h: X to E$$ between compact, connected and complex analytic varieties $$p: tilde {E} to E$$ to be universal coverage, and denote by $$tilde {h}: tilde {X} to tilde {E}$$ the withdrawal of $$h$$ via $$p$$.

So why do $$h$$ and $$tilde {h}$$ have the same fibers? Since $$tilde {X}$$ is the cover space of $$X$$, should not the fiber of $$h$$ to be the quotient of the fiber of $$tilde {h}$$?

The declaration is from here p.4, last paragraph.