Results on the algebraic matroid of the determinantal variety

• URL: http://arxiv.org/abs/2002.05082v6
• Date: Sun, 19 Sep 2021 08:15:05 GMT
• Title: Results on the algebraic matroid of the determinantal variety
• Authors: Manolis C. Tsakiris
• Abstract summary: We present a family of base sets of the matroid and conjecture these are all the base sets. This conjecture is reduced to a purely statement, which is proved for special cases.
• Score: 16.54912614895861
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We make progress towards characterizing the algebraic matroid of the determinantal variety. We present a family of base sets of the matroid and conjecture these are all the base sets. This conjecture is reduced to a purely combinatorial statement, which is proved for special cases. Our results rely on the combinatorial notion of relaxed supports of linkage matching fields that we introduce, our interpretation of the problem of completing a matrix of bounded rank from a subset of its entries as a linear section problem on the Grassmannian, and a connection that we draw with a class of local coordinates on the Grassmannian described by Sturmfels $\&$ Zelevinsky.

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