Matrix factorizations and curves in $\mathbb{P}^4$
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 BrillNoether 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2016
 DOI:
 10.48550/arXiv.1611.03669
 arXiv:
 arXiv:1611.03669
 Bibcode:
 2016arXiv161103669S
 Keywords:

 Mathematics  Algebraic Geometry
 EPrint:
 Minor corrections and a few additional comments made. Accepted for publication in Doc. Math