An explicit matrix factorization of cubic hypersurfaces of small dimension
Algebraic Geometry
2019-10-31 v2 Commutative Algebra
Abstract
In this paper, we compute an explicit matrix factorization of a rank 9 Ulrich sheaf on a general cubic hypersurface of dimension at most 7, whose existence was proved by Manivel. Instead of using invariant theory, we use Shamash's construction with a cone over the spinor variety. We also describe an algebro-geometric interpretation of our matrix factorization which connects the spinor tenfold and the Cartan cubic.
Keywords
Cite
@article{arxiv.1905.09626,
title = {An explicit matrix factorization of cubic hypersurfaces of small dimension},
author = {Yeongrak Kim and Frank-Olaf Schreyer},
journal= {arXiv preprint arXiv:1905.09626},
year = {2019}
}
Comments
18 pages, with Macaulay2 scripts. Fixed some typos, and updated a few references