Geodesic
Matrix Factorizations and Curves in $\mathbb{P}^4$
Documenta mathematica, Tome 23 (2018), pp. 1895-1924.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 14H10, 14M20, 14Q05, 13D02
Keywords: matrix factorization, moduli of curves, unirationality, Hurwitz space 
@article{DOCMA_2018__23__a9,
     author = {Schreyer, Frank-Olaf and Tanturri, Fabio},
     title = {Matrix {Factorizations} and {Curves} in $\mathbb{P}^4$},
     journal = {Documenta mathematica},
     pages = {1895--1924},
     publisher = {mathdoc},
     volume = {23},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a9/}
}
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Schreyer, Frank-Olaf; Tanturri, Fabio. Matrix Factorizations and Curves in $\mathbb{P}^4$. Documenta mathematica, Tome 23 (2018), pp. 1895-1924. http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a9/