Identifiability of homogeneous polynomials and Cremona transformations

Abstract

Abstract A homogeneous polynomial of degree d in n + 1 {n+1} variables is identifiable if it admits a unique additive decomposition in powers of linear forms. Identifiability is expected to be very rare. In this paper we conclude a work started more than a century ago and we describe all values of d and n for which a general polynomial of degree d in n + 1 {n+1} variables is identifiable. This is done by classifying a special class of Cremona transformations of projective spaces.