This package provides functions that construct g-nodal canonical curves with a degree k line bundle, which lie on a normalized scroll. It furthermore contains functions that compute the so-called relative canonical resolution. The construction of such canonical curves is based on the Macaulay2 package kGonalNodalCurves. This package can be seen as an upgrade to the kGonalNodalCurves package.## Construction of relative canonical resolutions

## Iterated mapping cones and Eagon-Nortcott type complexes

We also provide functions to compute (possibly non-minimal) free resolutions of such curves by an iterated mapping cone construction, as described in Schreyer's article Syzygies of Canonical Curves and Special Linear Series.

- canCurveWithFixedScroll -- Computes a g-nodal canonical curve with a degree k line bundle on a normalized scroll
- curveOnScroll -- Computes the ideal of a canonical curve on a normalized scroll in terms of generators of the scroll
- resCurveOnScroll -- Computes the relative canonical resolution

- eagonNorthcottType -- Computes the Eagon-Northcott type resolution
- liftMatrixToEN -- Lifts a matrix between bundles on the scroll to the associated Eagon-Northcott type complexes
- iteratedCone -- Computes a (possibly non-minimal) resolution of C in P^{g-1} starting from the relative canonical resolution of C in P(E)

This package requires Macaulay2 Version 1.11 or newer.

- Functions and commands
- balancedPartition -- Computes balanced partition of n of length d
- canCurveWithFixedScroll -- Computes a g-nodal canonical curve with a degree k line bundle on a normalized scroll
- canonicalMultipliers -- Computes the canonical multipliers of a rational curves with nodes
- curveOnScroll -- Computes the ideal of a canonical curve on a normalized scroll in terms of generators of the scroll
- eagonNorthcottType -- Computes the Eagon-Northcott type resolution
- getCoxDegrees -- Computes the degree of a polynomial in the Cox ring corresponding to a section of a bundle on the scroll
- getScrollDegrees -- Computes the degree of a section of a bundle on the scroll ring corresponding to a polynomial in the Cox ring
- iteratedCone -- Computes a (possibly non-minimal) resolution of C in P^{g-1} starting from the relative canonical resolution of C in P(E)
- liftMatrixToEN -- Lifts a matrix between bundles on the scroll to the associated Eagon-Northcott type complexes
- lineBundleFromPointsAndMultipliers -- Computes basis of a line bundle from the 2g points P_i, Q_i and the multipliers
- resCurveOnScroll -- Computes the relative canonical resolution
- rkSyzModules -- Computes the rank of the i-th module in the relative canonical resolution