Identifiability of homogeneous polynomials and Cremona transformations

By Francesco Galuppi, Massimiliano Di Mella. Journal für die Reine und Angewandte Mathematik, 2016

49 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/6baae870744f6fe730c003986e563c995901829b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Alessandra Bernardi
2. M. Catalisano
3. A. Oneto
4. Alessandro Gimigliano
5. Enrico Carlini

In Geometry and Topology

1. A. Oneto
2. M. Catalisano
3. Alessandro Gimigliano
4. Alessandra Bernardi
5. Enrico Carlini

Citations in the corpus

• The Hitchhiker Guide to: Secant Varieties and Tensor Decomposition (2018, background): “Recently, Galuppi and Mella proved that these are the only generically identifiable cases when considering symmetric-ranks of symmetric tensors; see [203].”