Duke Mathematical Journal

The Prym–Green conjecture for torsion line bundles of high order

Gavril Farkas and Michael Kemeny

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Abstract

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 $C$ of odd genus $g$ and order $\ell\geq\sqrt{\frac{g+2}{2}}$ 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 $\ell$-torsion line bundle in a linear system on a special K3 surface.

Article information

Source
Duke Math. J. Volume 166, Number 6 (2017), 1103-1124.

Dates
Received: 25 October 2015
Revised: 15 July 2016
First available in Project Euclid: 16 December 2016

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1481879046

Digital Object Identifier
doi:10.1215/00127094-3792814

Subjects
Primary: 14H
Secondary: 14H10: Families, moduli (algebraic)

Keywords
paracanonical curve Koszul cohomology natural resolution Barth–Verra surface

Citation

Farkas, Gavril; Kemeny, Michael. The Prym–Green conjecture for torsion line bundles of high order. Duke Math. J. 166 (2017), no. 6, 1103--1124. doi:10.1215/00127094-3792814. http://projecteuclid.org/euclid.dmj/1481879046.


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