This package implements the methods of the paper 'Unirational component of moduli spaces of 6-gonal genus 11 curves' and serves as supporting code for the computational proofs it contains.
random6gonalGenus11CurveExtraPencil -- triple cover of an elliptic curve with a distinguished extra pencil of degree 6 with Betti number B(5,6)=30.
Scrolls swept out by pencils
scrollsPencilOfLinesDouble -- compute the list of scrolls swept out by pencil of lines through each of double points
scrollsPencilOfLinesTriple -- compute the list of scrolls swept out by pencil of lines through each of triple points
scrollPencilOfConics4Triple -- compute the ideal of the scroll swept out by the pencil of conics through the 4 triple points
scrollPencilOfCubicsFixedPoints -- compute the ideals of the scrolls swept out by the pencils g^1_{6}'s induced by the pencil of cubics through the 8 singular points
injectiveMapScrollCanCurve -- injective map of chain complexes from resolution of the scroll to the linear stand of minimal resolution of canonical curve
equisingularDefCurveNodes -- compute the first order embedded deformations of a canonical curve induced by equisingular deformations of its nodal plane model
equisingularDefCurveTriples -- compute the first order embedded deformations of a canonical curve induced from equisingular deformations of its plane model with triple and double singular points
Verify all the assertions of paper
verifyAssertion -- print commands to verify the assertions of the paper
Caveat
This package requires Macaulay2 Version 1.10 or newer and the package FirstOrderDeformations.m2 by the authors, which should be installed before this one.
equisingularDefCurveNodes -- compute the first order embedded deformations of a canonical curve induced by equisingular deformations of its nodal plane model
equisingularDefCurveTriples -- compute the first order embedded deformations of a canonical curve induced from equisingular deformations of its plane model with triple and double singular points
injectiveMapScrollCanCurve -- injective map of chain complexes from resolution of the scroll to the linear stand of minimal resolution of canonical curve
scrollPencilOfConics4Triple -- compute the ideal of the scroll swept out by the pencil of conics through the 4 triple points
scrollPencilOfCubicsFixedPoints -- compute the ideals of the scrolls swept out by the pencils g^1_{6}'s induced by the pencil of cubics through the 8 singular points
scrollsPencilOfLinesDouble -- compute the list of scrolls swept out by pencil of lines through each of double points
scrollsPencilOfLinesTriple -- compute the list of scrolls swept out by pencil of lines through each of triple points