On the ranks of homogeneous polynomials of degree at least 9 and border rank 5
Abstract
Let
be a degree
homogenous polynomial with border rank
. We prove that it has rank at most
and give better results when
essentially depends on at most
variables or there are other conditions on the scheme evincing the cactus and border rank of
. We always assume that
essentially depends on at most
variables, because the other case was done by myself in Acta Math. Vietnam. 42 (2017), 509-531.
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DOI Code:
10.1285/i15900932v38n2p55
Keywords:
symmetric tensor rank; border rank; cactus rank
Full Text: PDF