• 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}
}
. 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

. 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

. 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

References

SHOWING 1-10 OF 11 REFERENCES

Ultrahomogeneous tensor spaces

. 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

Pencils of Quadrics: Old and New

Two-dimensional linear spaces of symmetric matrices are classified by Segre symbols. After reviewing known facts from linear algebra and projective geometry, we address new questions motivated by

Properties of High Rank Subvarieties of Affine Spaces

We use tools of additive combinatorics for the study of subvarieties defined by high rank families of polynomials in high dimensional Fq\documentclass[12pt]{minimal} \usepackage{amsmath}

Topological Noetherianity of polynomial functors

  • J. Draisma
  • Mathematics
    Journal of the American Mathematical Society
  • 2019
We prove that any finite-degree polynomial functor over an infinite field is topologically Noetherian. This theorem is motivated by the recent resolution, by Ananyan-Hochster, of Stillman’s

Big polynomial rings and Stillman’s conjecture

Ananyan-Hochster's recent proof of Stillman's conjecture reveals a key principle: if $f_1, \dots, f_r$ are elements of a polynomial ring such that no linear combination has small strength then $f_1,

Small subalgebras of polynomial rings and Stillman’s Conjecture

It is shown that in a polynomial ring of arbitrary characteristic, any <inline-formula content-type="math/mathml" xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K"> <mml:semantics> .

Topological noetherianity for cubic polynomials

Let P3(k∞) be the space of cubic polynomials in infinitely many variables over the algebraically closed field k (of characteristic ≠ 2, 3). We show that this space is GL∞-noetherian, meaning that any

On elementary equivalence, isomorphism and isogeny

Motive par un travail recent de Florian Pop, nous etudions les liens entre trois notions d'equivalence pour des corps de fonctions: isomorphisme, equivalence elementaire et la condition que les deux

Ideals Generated by Quadratic Polynomials

Let $R$ be a polynomial ring in $N$ variables over an arbitrary field $K$ and let $I$ be an ideal of $R$ generated by $n$ polynomials of degree at most 2. We show that there is a bound on the