On quartic double fivefolds and the matrix factorizations of exceptional quaternionic representations

We describe a remarkable rank 14 matrix factorization of the octic Spin 14 -invariant polynomial on either of its half-spin representations. We observe that this representation can be, in a suitable sense, identified with a tensor product of two octonion algebras. Moreover the matrix factorisation can be deduced from a particular Z-grading of e 8 . Intriguingly, the whole story can in fact be extended to the whole Freudenthal-Tits magic square and yields matrix factorizations on other spin representations, as well as for the degree seven invariant on the space of three-forms in several variables. As an application of our results on Spin 14 , we construct a special rank seven vector bundle on a double-octic threefold, that we conjecture to be spherical.

show abstract

Hodge numbers and Hodge structures for 3-Calabi–Yau categories

Abuaf

2023

Annales De La Faculté Des Sciences De Toulouse : Mathématiques

Self Cite

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

On quartic double fivefolds and the matrix factorizations of exceptional quaternionic representations

Abstract: Les Annales de l'institut Fourier sont membres du Centre Mersenne pour l'édition scienti que ouverte www.centre-mersenne.org

Cited by 3 publications

References 18 publications

On the Twisted Octonionic Eigenvalue Problem and Some Sextics Hypersurfaces Related to the Cartan Cubic

On the Twisted Octonionic Eigenvalue Problem and Some Sextics Hypersurfaces Related to the Cartan Cubic

Gradings of Lie algebras, magical spin geometries and matrix factorizations

Hodge numbers and Hodge structures for 3-Calabi–Yau categories

Contact Info

Product

Resources

About