Suppose $X$ and $Y$ are two varieties over $\mathbb C$, and $f:X\to Y$ is a proper smooth morphism. Fix any $y\in Y$, and denote $X_y$ the fiber over $y$. Can we get an action of $\pi_1(Y,y)$ on $X_y$? Maybe there needs some kind of "parallel transport"?
2026-04-03 00:59:01.1775177941
Monodromy action on the fiber
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