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arXiv · 1611.03669

Matrix factorizations and curves in $\mathbb{P}^4$

Frank-Olaf Schreyer·Fabio Tanturri
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Abstract

Let $C$ be a curve in $\mathbb{P}^4$ and $X$ be a hypersurface containing it. We show how it is possible to construct a matrix factorization on $X$ from the pair $(C,X)$ and, conversely, how a matrix factorization on $X$ leads to curves lying on $X$. We use this correspondence to prove the unirationality of the Hurwitz space $\mathcal{H}_{12,8}$ and the uniruledness of the Brill-Noether space $\mathcal{W}^1_{13,9}$. Several unirational families of curves of genus $16 \leq g \leq 20$ in $\mathbb{P}^4$ are also exhibited.

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Frank-Olaf Schreyer, Fabio Tanturri. 2016-11-11. Matrix factorizations and curves in $\mathbb{P}^4$. https://doi.org/10.25537/dm.2018v23.1895-1924

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