The resolution of paracanonical curves of odd genus

TL;DR

This paper proves the Prym-Green conjecture for all levels in odd genus by using decomposable ruled surfaces over elliptic curves, providing a complete solution to the problem.

Contribution

It offers the first complete proof of the Prym-Green conjecture for all levels in odd genus using a novel geometric approach.

Findings

Confirmed the Prym-Green conjecture for all levels in odd genus.

Developed a new method involving decomposable ruled surfaces over elliptic curves.

Established a comprehensive understanding of the resolution of paracanonical curves in odd genus.

Abstract

The Prym-Green conjecture predicts that the resolution of a general level p paracanonical curve of genus g is natural. Using decomposable ruled surfaces over an elliptic curve, we provide a complete solution (that is, for all levels) to this conjecture in odd genus.