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

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

Authors: 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
    Published on: September 1, 2017
    Accepted on: July 26, 2017
    Submitted on: July 26, 2017
    Keywords: Mathematics - Algebraic Geometry,Mathematics - Commutative Algebra

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