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.
Syzygies of Prym and paracanonical curves of genus 8 / E. Colombo, G. Farkas, A. Verra, C. Voisin. - (2016 Dec 03).
|Titolo:||Syzygies of Prym and paracanonical curves of genus 8|
COLOMBO, ELISABETTA (Primo)
|Settore Scientifico Disciplinare:||Settore MAT/03 - Geometria|
|Data di pubblicazione:||2016-12-03|
|Appare nelle tipologie:||24 - Pre-print|