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arXiv · 2305.06470

Upper bounds for the rank of powers of quadrics

Cosimo Flavi
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Abstract

We establish an upper bound for the rank of every power of an arbitrary quadratic form. Specifically, for any $s\in\mathbb{N}$, we prove that the $s$-th power of a quadratic form of rank $n$ grows as $n^s$. Furthermore, we demonstrate that its rank is subgeneric for all $n>(2s-1)^2$.

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Cosimo Flavi. 2023-05-10. Upper bounds for the rank of powers of quadrics. https://arxiv.org/abs/2305.06470

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