Definition 29.56.1. Let $f : X \to Y$ be a morphism of schemes.

We say the integer $n$

*bounds the degrees of the fibres of $f$*if for all $y \in Y$ the fibre $X_ y$ is a finite scheme over $\kappa (y)$ whose degree over $\kappa (y)$ is $\leq n$.We say the

*fibres of $f$ are universally bounded*^{1}if there exists an integer $n$ which bounds the degrees of the fibres of $f$.

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