# Isogeny classes of cubic spaces

@inproceedings{Bik2022IsogenyCO, title={Isogeny classes of cubic spaces}, author={Arthur Bik and Alessandro Danelon and Andrew Snowden}, year={2022} }

. 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

### Ultrahomogeneous tensor spaces

- 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…

### Matrix factorizations of generic polynomials

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- 2021

. 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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