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Syzygies of Prym and paracanonical curves of genus 8

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arxiv 1612.01026 v2 pith:JJBXWD4U submitted 2016-12-03 math.AG math.AC

Elisabetta Colombo , Gavril Farkas , Alessandro Verra , Claire Voisin This is my paper · ORCID
classification math.AGmath.AC
keywords conjecturegenusprym-greencurveslevelparacanonicalsyzygiesalmost
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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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  1. The Geometric Syzygy Conjecture in Positive Characteristic

    math.AG 2025-08 conditional novelty 7.0 of 10

    The Geometric Syzygy Conjecture holds for general canonical curves over algebraically closed fields of characteristic at least 2g-4.

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