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NodalCurves :: NodalCurves

NodalCurves -- construction of nodal rational curves


What’s new: Minor corrections

Version 0.4.

Overview: Starting from a collection of g pairs of points Pi, Qi the canonical image of the rational curves with nodes at these points is constructed. Similarly, embedding of these curves by the linear series K ⊗L with L an n-torsion bundle is constructed.

One main goal is to verify two conjectures. Conjecture A is the Prym-Green Conjecture on syzygies of Prym canonical curves of even genus g and level n, see Farkas, Ludwig [2008] for small values of g and level n. This works up to genus 16 with the exception of genus (g,n)=(8,2) or (16,2). The case of genus 16 requires a lot of time and memory.

Conjecture B, see Chiodo, Eisenbud, Farkas, Schreyer [2012] (HREF has to be corrected), concerns syzygies of torsion bundles Lk in Prym canonical space P(H0(C,K⊗L) again for curves of even genus.


This package requires Macaulay2 version 1.9 or newer.

Install this Package by doing





This documentation describes version 0.4.2 of NodalCurves.

Source code

The source code from which this documentation is derived is in the file NodalCurves.m2.