Matrix factorizations and curves in P4

Frank-Olaf Schreyer (1) , Fabio Tanturri (2)

1 Universität des Saarlandes
2 I2M - Institut de Mathématiques de Marseille

Let C be a curve in 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 H_12,8 and the uniruledness of the Brill-Noether space W^1_13,9. Several unirational families of curves of genus 16 ≤ g ≤ 20 in P^4 are also exhibited.

Domaines: Mathématiques [math]; Géométrie algébrique [math.AG]

Frank-Olaf Schreyer, Fabio Tanturri. Matrix factorizations and curves in P4. Documenta Mathematica, 2018, 23, pp.1895-1924. ⟨10.25537/dm.2018v23.1895-1924⟩. ⟨hal-01396676⟩