Algebraic boundary of matrices of nonnegative rank at most three
  The Zariski closure of the boundary of the set of matrices of nonnegative rank at most 3 is reducible. We give a minimal generating set for the ideal of each irreducible component. In fact, this generating set is a Grobner basis with respect to the graded reverse lexicographic order. This solves a conjecture by Robeva, Sturmfels and the last author. 
Rob H. Eggermont, Emil Horobet and Kaie Kubjas
math.AG math.AC math.RT