Files for "Gröbner techniques for low degree Hilbert stability," by Morrison and Swinarski

• Code samples

• Additional Macaulay 2 functions
  This file contains several functions not in the Macaulay 2 package StatePolytope version 1.1. Notably, the functions "subhp" (a much faster function for computing Hilbert points) and "mcStable," which is an implementation of a Monte Carlo strategy for testing GIT stability.

• Two points in P^2

• Twisted cubic

• Genus 3 Wiman curve
  This was one of our earliest calculations, before we automated the interfaces between the different packages we used.

• Genus 4 Wiman curve
  • Monte Carlo stability calculation
    The outputs following i5, i7, i9, i11, and i13 show that this curve is stable for m = 2, 3, 4, 5, 6, respectively.
    
  • A set of nine initial ideals that span the barycenter for several values of m, but not all the way up to the Gotzmann number
    
  • A set of nine initial ideals that span the barycenter for m=4 to 64
    

• Genus 5 Wiman curve
  • m=2,3,4,5,6,7 stability
    The outputs following i5, i7, i9, i11, i13, and i15 show that this curve is stable for m = 2, 3, 4, 5, 6, 7, respectively.
  • m=8,9 stability
    The outputs following i5, i7 show that this curve is stable for m = 8, 9, respectively.
  • m=4 to 11 stability
    This file shows that the 48 initial ideals which establish stability for m=7 actually establish stability for 4 <= m <= 11; here are the special commands used.

• Genus 6 Wiman curve
  • m=2 stability
    
  • m=3 stability
    
  • m=4, 5, 6, 7 stability
    
  • m=8 stability
    

• Genus 7 Wiman curve
  • m=2, 3, 4, 5, 6, 7 stability
    

• Genus 8 Wiman curve
  • m=2, 3, 4, 5, 6, 7 stability
    

• An elliptic bridge
  A nodal genus 5 consisting of a genus two component connected to a genus 1 component connected to a genus 2 component

• A Weierstrass genus 2 tail
  A nodal genus 5 curve consisting of genus 3 Wiman curve glued to a genus 2 Wiman curve attached at a Weierstrass point
  • m=6 stability
    The output following i13 shows that this curve is semistable for m=6. The output following i5, i7, i9, i11 are evidence that this curve is unstable for m=2,3,4,5, as expected. The output following i15 shows that we didn't find initial ideals spanning the barycenter for m=7 with the number of Monte Carlo tries allowed. But in the following file, we succeed with more tries.
  • m=7 stability

• A general genus 2 tail
  A nodal genus 5 curve consisting of genus 3 Wiman curve glued to a genus 2 Wiman curve attached at a non-Weierstrass point
  • m=5 stability
    
  • m=6 stability
    
  • m=7 stability
    The last calculation in this file shows m=7 stability. The other calculations show that stability was not established in degrees less than 7. For m=2,3,4 this is because this curve is unstable. For m=5,6 we just didn't use enough random weights; see the previous two files for these cases.

• Genus 4 ribbon
  Here we examine an example of a genus 4 ribbon given in a paper of Bayer and Eisenbud. Our calculations indicate that it is Hilbert unstable but Chow semistable.