Geodesic
Syzygies of Prym and paracanonical curves of genus 8
Épijournal de Géométrie Algébrique, Tome 1 (2017)

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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. 
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     title = {Syzygies of {Prym} and paracanonical curves of genus 8},
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Colombo, Elisabetta; Farkas, Gavril; Verra, Alessandro; Voisin, Claire. Syzygies of Prym and paracanonical curves of genus 8. Épijournal de Géométrie Algébrique, Tome 1 (2017). doi: 10.46298/epiga.2017.volume1.2602

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