Abstract: We study some problems on symbolic powers of squarefree monomial ideals via polarizations. One of the main results we present is a short, simple and elementary proof of the following theorem by Minh-Trung, Varbaro and Terai-Trung characterizing matroids in an algebraic way: A simplicial complex is a matroid if and only if there exists an m>2 such that I^{(m)} is Cohen--Macaulay, where I is the Stanley—Reisner ideal of the simplicial complex.
We will discuss a few other proofs simplified by this approach and some natural questions which arise along the way.
This talk is based on joint work with Justin Lyle.
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