Bibliographic Details
| Title: |
Apolarity and direct sum decomposability of polynomials |
| Authors: |
Buczyńska, Weronika, Buczyński, Jarosław, Kleppe, Johannes, Teitler, Zach |
| Publication Year: |
2013 |
| Collection: |
Mathematics |
| Subject Terms: |
Mathematics - Algebraic Geometry, Mathematics - Commutative Algebra, 13H10, 14N15 |
| More Details: |
A polynomial is a direct sum if it can be written as a sum of two non-zero polynomials in some distinct sets of variables, up to a linear change of variables. We analyze criteria for a homogeneous polynomial to be decomposable as a direct sum, in terms of the apolar ideal of the polynomial. We prove that the apolar ideal of a polynomial of degree $d$ strictly depending on all variables has a minimal generator of degree $d$ if and only if it is a limit of direct sums.
Comment: 35 pages. v2: added remarks generalizing results to arbitrary characteristic. v3: extensive rewrite, several generalizations in last section, numerous clarifications throughout. v4: another extensive rewrite with improved notation and terminology, clarifications and corrections throughout, to incorporate suggestions of referee |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/1307.3314 |
| Accession Number: |
edsarx.1307.3314 |
| Database: |
arXiv |
