Using a construction of Barth and Verra that realizes torsion bundles on sections of special K3 surfaces, we prove that the minimal resolution of a general paracanonical curve of odd genus and order is natural, thus proving the Prym–Green conjecture. In the process, we confirm the expectation of Barth and Verra concerning the number of curves with -torsion line bundle in a linear system on a special K3 surface.
"The Prym–Green conjecture for torsion line bundles of high order." Duke Math. J. 166 (6) 1103 - 1124, 15 April 2017. https://doi.org/10.1215/00127094-3792814