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MatFac15 :: MatFac15

MatFac15 -- Constructions of curves of genus 15

Description

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

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

Main steps in the computation

Construction of families

  • 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

All assertions of the paper

Creation of candidate modules

  • 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

Author

Version

This documentation describes version 0.8 of MatFac15.

Source code

The source code from which this documentation is derived is in the file MatFac15.m2.

Exports

  • Functions and commands
  • Symbols
    • attempts -- optional argument in randomCurvesOfGenus15
    • certify -- optional argument in randomCurvesOfGenus15
    • printTimings (missing documentation)