Description
This package provides functions that construct g-nodal canonical curves with a degree k line bundle that lie on a normalized scroll. It furthermore contains functions that compute the 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.
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.
Construction of relative canonical resolutions
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canCurveWithFixedScroll -- Computes a g-nodal canonical curve with a degree k line bundle on a normalized scroll
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curveOnScroll -- Computes the ideal of a canonical curve on a normalized scroll in terms of generators of the scroll
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resCurveOnScroll -- Computes the relative canonical resolution
Iterated mapping cones and Eagon-Nortcott type complexes
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eagonNorthcottType -- Computes the Eagon-Northcott type resolution
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liftMatrixToEN -- Lifts a matrix between bundles on the scroll to the associated Eagon-Northcott type complexes
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iteratedCone -- Computes a (possibly non-minimal) resolution of C in P^{g-1} starting from the relative canonical resolution of C in P(E)