Algebraic boundary of matrices of nonnegative rank at most three

摘要

The Zariski closure of the boundary of the set of matrices of nonnegativerank at most 3 is reducible. We give a minimal generating set for the ideal ofeach irreducible component. In fact, this generating set is a Grobner basiswith respect to the graded reverse lexicographic order. This solves aconjecture by Robeva, Sturmfels and the last author.