what is the constant field of irreducible components a divisor?

Question

Let $D$ be a divisor on an algebraic variety over a field $k$, that is $$ D=\sum n_i D_i $$ where $D_i$ are the irreducible components. I came across the expression "the constant field of $D_i$" and I would like to know what does it means. I guess it has to do with the residue field of $\mathcal{O}_{X, \xi}$ where $\xi$ is the generic point of $D_i$, but what is the precise relationship? Thanks!

Answer 1

A reasonable definition would be: "constant field" = the algebraic closure of $k$ in the residue field $k(\xi)$ (equal to the function field of $D_i$).