Abstract: A finite set of elements in a field extension L/K defines a matroid via algebraic independence. From the perspective of algebraic geometry, every irreducible variety X in C^N therefore determines an algebraic matroid of rank dim(X) through the field extension C(X)/C. The bases of this matroid correspond precisely to coordinate projections that are branched covers.

This geometric perspective enriches the structure of algebraic matroids: bases and circuits carry natural degrees, and additionally, bases come equipped with a Galois (or monodromy) group. We describe these connections between algebraic matroids and algebraic geometry and make the case that numerical algebraic geometry is a powerful computational framework for handling such objects.

We end with two (open) examples of families of algebraic varieties whose matroids remain unknown.