Some examples of forms of high rank

Jarosław Buczyński; Zach Teitler

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arXiv · 1503.08253

Some examples of forms of high rank

Jarosław Buczyński·Zach Teitler

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Abstract

We describe some forms with greater Waring rank than previous examples. In $3$ variables we give forms of odd degree with strictly greater rank than the ranks of monomials, the previously highest known rank. This narrows the possible range of values of the maximum Waring rank of forms in $3$ variables. In $4$ variables we give forms of odd degree with strictly greater than generic rank. In degrees greater than or equal to $5$ these are the first examples showing that there exist forms with Waring rank strictly greater than the generic value.

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Jarosław Buczyński, Zach Teitler. 2015-03-28. Some examples of forms of high rank. https://arxiv.org/abs/1503.08253

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