This package implements the methods of the paper 'Matrix factorizations and curves in P^4' and serves as supporting code for the computational proofs it contains. The code needed to verify all the assertions of the paper is provided, as well as an output of its execution.## Main functions

## Construction of curves

## Betti candidates

## Verify all the assertions of the paper

- matrixFactorizationFromModule -- a matrix factorization induced by a quotient ring on a supporting hypersurface
- idealFromMatFac -- the ideal of a curve constructed from a matrix factorization
- isSmoothCurve -- check whether an ideal defines a smooth curve
- h1NormalBundle -- computes h^1 of the normal sheaf
- alexanderSurface -- construct an Alexander surface
- linSysAlexander -- linear systems giving rise to curves of genus >= 16 on the Alexander surface
- properTransformAlexander -- proper transform on the Alexander surface
- auxiliarLineBundle -- restriction of Omega(1) to a curve

- singularCurveInP4 -- nodal curve in P^4 of genus g and degree d
- curveGenus12Degree14InP4 -- curve in P^4 of genus 12 and degree 14
- curveGenus13Degree15InP4 -- curve in P^4 of genus 13 and degree 15
- randomCurveGenus10Degree13InP4 -- general curve in P^4 of genus 10 and degree 13
- randomCurveGenus12Degree14InP4 -- general curve in P^4 of genus 12 and degree 14
- randomGenus12Degree8CoverOfP1 -- general canonical curve of genus 12 with a g^1_8
- curveOnAlexanderSurface -- curves on the Alexander surface

- isInBoijSoederbergCone -- check whether a Betti table is in the Boij-Soederberg cone
- listOfPossibleMatFac -- different shapes of the same matrix factorization
- candidateTables -- Betti candidates for a given shape of a matrix factorization
- candidateTablesWithIrrelevantIdealAssociated -- Betti candidates with pd=5 for a given shape of a matrix factorization
- arisingMatFac -- shape of the arising matrix factorization assuming all possible cancellations
- precompiledListOfCandidates -- list of Betti candidates for curve of genus g >= 16

- verifyAssertionsOfThePaper -- print commands to verify the assertions of the paper

This package requires Macaulay2 Version 1.8 or newer and the package kGonalNodalCurves.m2 by Christian Bopp, which should be installed before this one.

- Functions and commands
- alexanderSurface -- construct an Alexander surface
- arisingMatFac -- shape of the arising matrix factorization assuming all possible cancellations
- auxiliarLineBundle -- restriction of Omega(1) to a curve
- candidateTables -- Betti candidates for a given shape of a matrix factorization
- candidateTablesWithIrrelevantIdealAssociated -- Betti candidates with pd=5 for a given shape of a matrix factorization
- curveGenus12Degree14InP4 -- curve in P^4 of genus 12 and degree 14
- curveGenus13Degree15InP4 -- curve in P^4 of genus 13 and degree 15
- curveOnAlexanderSurface -- curves on the Alexander surface
- h1NormalBundle -- computes h^1 of the normal sheaf
- idealFromMatFac -- the ideal of a curve constructed from a matrix factorization
- isInBoijSoederbergCone -- check whether a Betti table is in the Boij-Soederberg cone
- isSmoothCurve -- check whether an ideal defines a smooth curve
- linSysAlexander -- linear systems giving rise to curves of genus >= 16 on the Alexander surface
- listOfPossibleMatFac -- different shapes of the same matrix factorization
- matrixFactorizationFromModule -- a matrix factorization induced by a quotient ring on a supporting hypersurface
- precompiledListOfCandidates -- list of Betti candidates for curve of genus g >= 16
- properTransformAlexander -- proper transform on the Alexander surface
- randomCurveGenus10Degree13InP4 -- general curve in P^4 of genus 10 and degree 13
- randomCurveGenus12Degree14InP4 -- general curve in P^4 of genus 12 and degree 14
- randomGenus12Degree8CoverOfP1 -- general canonical curve of genus 12 with a g^1_8
- singularCurveInP4 -- nodal curve in P^4 of genus g and degree d
- verifyAssertionsOfThePaper -- print commands to verify the assertions of the paper