Finiteness of fibers in matrix completion via Plucker coordinates

Abstract: We describe a family of maximal elements of the algebraic matroid of the determinantal variety of at most rank-r matrices of size m x n over an infinite field k. For this, we formulate matrix completion as a hyperplane sections problem on the Grassmannian Gr(r,m) and use a family of local coordinates on Gr(r,m) induced by linkage matching fields, as described by Sturmfels & Zelevinsky (1993). Along the way we prove a conjecture of Rong, Wang & Xu (2019).

combinatorics

Audience: researchers in the topic

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Virtual seminar on algebraic matroids and rigidity theory

Series comments: The COVID-19 pandemic is forcing us all to stay home, foregoing conferences and departmental seminars for the next few months. This weekly virtual seminar is an attempt to patch that departmental-seminar-sized void in our lives until it is safe to resume our more traditional forms of professional networking. Since geographic location matters a lot less for a virtual seminar than for an in-person seminar, this virtual seminar will be defined purely by its mathematical theme, algebraic matroids and rigidity theory, and not any particular department nor region.