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

epiga:3815 - Épijournal de Géométrie Algébrique, 1 septembre 2017, Volume 1
Syzygies of Prym and paracanonical curves of genus 8

Auteurs : Colombo, Elisabetta and Farkas, Gavril and Verra, Alessandro and Voisin, Claire

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.


Source : oai:arXiv.org:1612.01026
Volume : Volume 1
Publié le : 1 septembre 2017
Déposé le : 26 juillet 2017
Mots-clés : Mathematics - Algebraic Geometry,Mathematics - Commutative Algebra


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