Using the method of Matrix factorizations and families of curves of genus 15 we construct via matrix factorization on cubics 3-folds in P^4 families of curves of genus 15.## Up to degree zero computations of Hom groups

## Main steps in the computation

## Construction of families

## All assertions of the paper

## Creation of candidate modules

- Hom0 -- compute the degree 0 part of a Hom group
- homomorphism0 -- compute the homomorphism corresponding to an element in Hom0

- matrixFactorizationFromModule -- compute a matrix factorization from a module
- curveFromMatrixFactorization -- compute the curve C associated to the matrix factorization
- isSmoothCurve -- check whether the ideal defines a smooth curve
- tangentKernelDimension -- compute the dimension of the kernel of the tangent map
- MCMapproximation -- compute the MCM approximation

- constructEx1 -- randomly choose a module N with Betti table as indicated in o4 below
- constructEx2 -- randomly choose a module N with Betti table as indicated in o4 below
- constructEx3 -- randomly choose a module N with Betti table as indicated in o4 below
- constructEx4 -- randomly choose a module N with Betti table as indicated in o4 below
- constructEx5 -- randomly choose a module N with Betti table as indicated in o4 below
- constructEx6 -- randomly choose a module N with Betti table as indicated in o4 below
- randomKRationalPoint -- Pick a random K rational point on the scheme X defined by I
- randomCurveOfGenus15 -- choose randomly a curve of genus 15

- verifyAllAssertionsOfThePaper -- print commands to verfy the assertions of the paper

- BSCandidates -- compute Boij-Soederberg points in the cone of resolution which could lead to the given a matrix factorization
- allCandidates -- compute the 39 integral points in the Boij-Soederberg

- Functions and commands
- allCandidates -- compute the 39 integral points in the Boij-Soederberg
- BSCandidates -- compute Boij-Soederberg points in the cone of resolution which could lead to the given a matrix factorization
- constructEx1 -- randomly choose a module N with Betti table as indicated in o4 below
- constructEx2 -- randomly choose a module N with Betti table as indicated in o4 below
- constructEx3 -- randomly choose a module N with Betti table as indicated in o4 below
- constructEx4 -- randomly choose a module N with Betti table as indicated in o4 below
- constructEx5 -- randomly choose a module N with Betti table as indicated in o4 below
- constructEx6 -- randomly choose a module N with Betti table as indicated in o4 below
- curveFromMatrixFactorization -- compute the curve C associated to the matrix factorization
- Hom0 -- compute the degree 0 part of a Hom group
- homomorphism0 -- compute the homomorphism corresponding to an element in Hom0
- isSmoothCurve -- check whether the ideal defines a smooth curve
- matrixFactorizationFromModule -- compute a matrix factorization from a module
- MCMapproximation -- compute the MCM approximation
- randomCurveOfGenus15 -- choose randomly a curve of genus 15
- randomKRationalPoint -- Pick a random K rational point on the scheme X defined by I
- tangentKernelDimension -- compute the dimension of the kernel of the tangent map
- verifyAllAssertionsOfThePaper -- print commands to verfy the assertions of the paper