An explicit matrix factorization of cubic hypersurfaces of small dimension

Yeongrak Kim; Frank-Olaf Schreyer

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arXiv · 1905.09626

An explicit matrix factorization of cubic hypersurfaces of small dimension

Yeongrak Kim·Frank-Olaf Schreyer

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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.

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Yeongrak Kim, Frank-Olaf Schreyer. 2019-10-30. An explicit matrix factorization of cubic hypersurfaces of small dimension. https://arxiv.org/abs/1905.09626

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