Elisabetta Colombo ; Gavril Farkas ; Alessandro Verra ; Claire Voisin - Syzygies of Prym and paracanonical curves of genus 8

epiga:2602 - Épijournal de Géométrie Algébrique, 1 septembre 2017, Volume 1 - https://doi.org/10.46298/epiga.2017.volume1.2602
Syzygies of Prym and paracanonical curves of genus 8Article

Auteurs : Elisabetta Colombo ; Gavril Farkas ; Alessandro Verra ; Claire Voisin

    By analogy with Green's Conjecture on syzygies of canonical curves, the Prym-Green conjecture predicts that the resolution of a general level p paracanonical curve of genus g is natural. The Prym-Green Conjecture is known to hold in odd genus for almost all levels. Probabilistic arguments strongly suggested that the conjecture might fail for level 2 and genus 8 or 16. In this paper, we present three geometric proofs of the surprising failure of the Prym-Green Conjecture in genus 8, hoping that the methods introduced here will shed light on all the exceptions to the Prym-Green Conjecture for genera with high divisibility by 2.


    Volume : Volume 1
    Publié le : 1 septembre 2017
    Accepté le : 26 juillet 2017
    Soumis le : 26 juillet 2017
    Mots-clés : Mathematics - Algebraic Geometry,Mathematics - Commutative Algebra

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