Real Rank Two Geometry
  The real rank two locus of an algebraic variety is the closure of the union of all secant lines spanned by real points. We seek a semi-algebraic description of this set. Its algebraic boundary consists of the tangential variety and the edge variety. Our study of Segre and Veronese varieties yields a characterization of tensors of real rank two. 
Anna Seigal and Bernd Sturmfels
math.AG cs.CG math.OC