Upper bounds for the rank of powers of quadrics
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917881605783552 |
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| author | Flavi, Cosimo |
| author_facet | Flavi, Cosimo |
| contents | 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 $n>(2s-1)^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_06470 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Upper bounds for the rank of powers of quadrics Flavi, Cosimo Algebraic Geometry 14N07 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 $n>(2s-1)^2$. |
| title | Upper bounds for the rank of powers of quadrics |
| topic | Algebraic Geometry 14N07 |
| url | https://arxiv.org/abs/2305.06470 |