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

1. 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 $\leq n$.

2. We say the fibres of $f$ are universally bounded1 if there exists an integer $n$ which bounds the degrees of the fibres of $f$.

[1] This is probably nonstandard notation.

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