Files related to the genus 5 nodal curve with an elliptic bridge
We obtained equations for each subcurve using Magma, and intersected the resulting ideals to obtain the ideal of the curve. This ideal is multiplicity free.
In the first basis
The first basis we wrote is not adapted to the decomposition into irreducibles, and thus, in the language of our paper, the torus scaling these variables does not determine stability. However, the generators of the ideal are rather simple in this basis (several monomials, only a few binomial and trinomial generators) and we therefore computed the state polytope in this basis anyway.
gfan produced all the initial ideals of the curve.
There are 500,094 initial ideals. Macaulay 2 only handles lists of length 50,000. Thus, to analyze our curve further, we split the list of initial ideals into 12 shorter lists.
We computed the Chow points for each of these lists and collected these in one Chow polytope file. We then tested whether this point spanned the barycenter of its ambient plane; it does. But as noted above, we are not justified in concluding from this calculation that this example is Chow semistable.
In the second basis
To confirm Hassett and Hyeon's result that the elliptic bridge is Chow strictly semistable, we switched into a basis adapted to the decomposition into irreducibles, and did a Monte Carlo calculation. Here are the special M2 commands used.