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arXiv · 1612.01026

Syzygies of Prym and paracanonical curves of genus 8

Elisabetta Colombo·Gavril Farkas·Alessandro Verra·Claire Voisin
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Abstract

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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Elisabetta Colombo, Gavril Farkas, Alessandro Verra, Claire Voisin. 2016-12-03. Syzygies of Prym and paracanonical curves of genus 8. https://doi.org/10.46298/epiga.2017.volume1.2602

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