Upper bounds for the rank of powers of quadrics

2023/05/10 by Cosimo Flavi, Flavi, Cosimo · 1 citation
Computer Science · Mathematics · #14N07 #Algebraic Geometry (math.AG) #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2305.06470

openalex publication_date 2023/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish an upper bound for the rank of every power of an arbitrary quadratic form. Specifically, for any s∈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.

Cited by

• Waring decompositions of the product of two quadrics: the small rank cases

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