# singletonSpineBasis -- computes the singleton spine basis of curves on M0nbar

## Synopsis

• Usage:
singletonSpineBasis(n)
• Inputs:
• Outputs:

## Description

The singleton spine basis of F-curves is described in notes by Swinarski, A basis of F-curves on $\bar{M}_{0,n}$, available at http://faculty.fordham.edu/dswinarski/Fcurves/.

It is defined for n>=7.

 i1 : B7=singletonSpineBasis(7) o1 = {CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1}, {2}, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ {3}, {4, 5, 6, 7}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1}, {2}, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ {3, 4, 5, 6}, {7}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1}, {2}, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ {3, 4, 5, 7}, {6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1}, {2}, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ {3, 4, 6, 7}, {5}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1}, {2}, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ {3, 5, 6, 7}, {4}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1}, {2, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 3}, {4, 5}, {6, 7}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1}, {2, 3, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 4, 5}, {6}, {7}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1}, {2, 3, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 4, 6}, {5}, {7}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1}, {2, 3, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 4, 7}, {5}, {6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1}, {2, 3, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 5, 6}, {4}, {7}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1}, {2, 3, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 5, 7}, {4}, {6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1}, {2, 3, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 6, 7}, {4}, {5}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1}, {2, 4, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 5, 6}, {3}, {7}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1}, {2, 4, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 5, 7}, {3}, {6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1}, {2, 4, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 6, 7}, {3}, {5}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1}, {2, 5, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 6, 7}, {3}, {4}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1, 2}, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ {3}, {4, 5}, {6, 7}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1, 2}, {3, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 4}, {5}, {6, 7}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1, 2}, {3, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 4}, {5, 6}, {7}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1, 2, 3, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 4}, {5}, {6}, {7}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1, 2, 3, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 5}, {4}, {6}, {7}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1, 2, 3, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 6}, {4}, {5}, {7}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1, 2, 3, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 7}, {4}, {5}, {6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1, 2, 4, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 5}, {3}, {6}, {7}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1, 2, 4, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 6}, {3}, {5}, {7}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1, 2, 4, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 7}, {3}, {5}, {6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1, 2, 5, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 6}, {3}, {4}, {7}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1, 2, 5, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 7}, {3}, {4}, {6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1, 2, 6, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 7}, {3}, {4}, {5}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1, 3, 4, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 5}, {2}, {6}, {7}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1, 3, 4, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 6}, {2}, {5}, {7}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1, 3, 4, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 7}, {2}, {5}, {6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1, 3, 5, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 6}, {2}, {4}, {7}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1, 3, 5, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 7}, {2}, {4}, {6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1, 3, 6, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 7}, {2}, {4}, {5}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1, 4, 5, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 6}, {2}, {3}, {7}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1, 4, 5, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 7}, {2}, {3}, {6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1, 4, 6, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 7}, {2}, {3}, {5}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1, 5, 6, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 7}, {2}, {3}, {4}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1, 7}, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ {2}, {3, 4}, {5, 6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1, 7}, {2, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 3}, {4}, {5, 6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1, 7}, {2, NumberOfMarkedPoints => 7 ------------------------------------------------------------------------ 3}, {4, 5}, {6}} => 1}}} o1 : List

## Ways to use singletonSpineBasis :

• "singletonSpineBasis(ZZ)"

## For the programmer

The object singletonSpineBasis is .