• Corpus ID: 251134883

# Isogeny classes of cubic spaces

```@inproceedings{Bik2022IsogenyCO,
title={Isogeny classes of cubic spaces},
author={Arthur Bik and Alessandro Danelon and Andrew Snowden},
year={2022}
}```
• Published 28 July 2022
• Mathematics
. A cubic space is a vector space equipped with a symmetric trilinear form. Two cubic spaces are isogeneous if each embeds into the other. A cubic space is non-degenerate if its form cannot be expressed as a ﬁnite sum of products of linear and quadratic forms. We classify non-degenerate cubic spaces of countable dimension up to isogeny: the isogeny classes are completely determined by an invariant we call the residual rank , which takes values in N ∪ {∞} . In particular, the set of classes is…
2 Citations
• Mathematics
• 2022
. A cubic space is a vector space equipped with a symmetric trilinear form. Using categorical Fra¨ıss´e theory, we show that there is a universal ultrahomogeneous cubic space V of countable inﬁnite
. We prove that the Buchweitz-Greuel-Schreyer Conjecture on the minimal rank of a matrix factorization holds for a generic polynomial of given degree and strength. The proof introduces a notion of

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