Grassmannian bundle: any good reference?

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I have met the notion of Grassmannian bundle of a vector bundle over a variety in intersection theory, but anywhere I look I just find a brief recall of how the stalks look like (my references so far are "3264 and all that" by Eisenbud and Harris, "Intersection Theory" by Fulton). I was wondering whether there is any good reference to see the actual definition and construction and the universal properties of this object...