Hypertree divisor classes

This is a database of hypertree divisor classes on the moduli space of stable rational curves with n marked points compiled by Morgan Opie. For information on these divisors, see Hypertrees, projections, and moduli of stable rational curves by Castravet and Tevelev and Extremal divisors on moduli spaces of rational curves with marked points by Opie.

Divisor classes corresponding to all hypertrees (up to permutation) on 6,7,8,9, and 10 vertices appear here. The hypertrees themselves were found by Ilya Scheidwasser as part of his UMass Amherst capstone.

The class given for a divisor in M̅ 0,n is actually that in the pull back to M̅ 0,n+1 under the forgetful morphism in index n+1. This index is used as the "special index" for the Kapranov basis of Cl(M̅ 0,n+1). A polynomial encodes a divisor as follows: a free generator EI = δI,n+1 is represented as a monomial ∏xi, for i in I. z corresponds to the class of a Kapranov hyperplane pullback.

For each n between 6 and 10, a .txt file with all divisors is ready to be downloaded and imported to Macaulay. A .pdf of each divisor in a more readable format is given. Symmetry group sizes were computed in Macaulay for n less than 9 (computations for n=9,10 took too long). For spherical hypertrees, as described in the paper of Castravet and Tevelev, sketches are included.

The Macaulay 2 program used to compute the class of a divisor in M̅ 0,n specified by a polynomial equation in n variables (as well as code specialized to hypertree and Chen-Coskun divisors) can be found here.
The code for computing symmetry groups is here.


n=6. All divisors.


n=7. All divisors.

n=8. All divisors.

n=9. All divisors.

n=10. All divisors.