What is a realizable matroid?

Question

In note I'm reading, there is a term called realizable matroid.

Prove that $\mathbb{k}$ is algebraically closed then $M$ is realizable over $\mathbb{k}$ if and only if the following identity of ideals holds:...

I have searched on the Internet, but I haven't found any definition or theorem about the realizability of a matroid.

So what is a realizable matroid?

Please explain for me.

Thanks.

Answer 1

After reading the linked notes(*) carefully, it would appear that the author uses the standard term "representable" and the nonstandard term "realizable" interchangeably.

(*) It's not an article, it's a set of class notes. These are certainly not to the same editorial standards as an article or a presentation at a conference.