@article{HIL-Equations-For-Lower-Bounds-On-Border-Rank,
Title = {Equations for lower bounds on border rank},
Author = {Jonathan David Hauenstein and Christian Ikenmeyer and Joseph Montague Landsberg},
Pages = {372--383},
Year = {2013},
Doi = {10.1080/10586458.2013.825892},
Journal = {Experimental Mathematics},
Volume = {22},
Number = {4},
Abstract = {We present new methods for determining polynomials in the ideal of the variety of bilinear maps of border rank at most $r$. We apply these methods to several cases including the case $r = 6$ in the space of bilinear maps $\mathbb C^4 \times \mathbb C^4 \to \mathbb C^4$. This space of bilinear maps includes the matrix multiplication operator $M_2$ for two by two matrices. We show these newly obtained polynomials do not vanish on the matrix multiplication operator $M_2$, which gives a new proof that the border rank of the multiplication of $2 \times 2$ matrices is seven. Other examples are considered along with an explanation of how to implement the methods.},
Url = {http://arxiv.org/abs/1305.0779},
Url2 = {http://www3.math.tu-berlin.de/algebra/work/1305.0779v2.pdf}
}