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

Synopsis

Usage:

singletonSpineBasis(n)
Inputs:
- n, an integer,
Outputs:
- a list,
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},
                                     "NumberOfMarkedPoints" => 7         
     ------------------------------------------------------------------------
     {2}, {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,
                                    "NumberOfMarkedPoints" => 7             
     ------------------------------------------------------------------------
     3, 4, 5}, {6}, {7}} => 1}},
                                
     ------------------------------------------------------------------------
     CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1}, {2,
                                    "NumberOfMarkedPoints" => 7             
     ------------------------------------------------------------------------
     3, 4, 6}, {5}, {7}} => 1}},
                                
     ------------------------------------------------------------------------
     CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1}, {2,
                                    "NumberOfMarkedPoints" => 7             
     ------------------------------------------------------------------------
     3, 4, 7}, {5}, {6}} => 1}},
                                
     ------------------------------------------------------------------------
     CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1}, {2,
                                    "NumberOfMarkedPoints" => 7             
     ------------------------------------------------------------------------
     3, 5, 6}, {4}, {7}} => 1}},
                                
     ------------------------------------------------------------------------
     CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1}, {2,
                                    "NumberOfMarkedPoints" => 7             
     ------------------------------------------------------------------------
     3, 5, 7}, {4}, {6}} => 1}},
                                
     ------------------------------------------------------------------------
     CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1}, {2,
                                    "NumberOfMarkedPoints" => 7             
     ------------------------------------------------------------------------
     3, 6, 7}, {4}, {5}} => 1}},
                                
     ------------------------------------------------------------------------
     CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1}, {2,
                                    "NumberOfMarkedPoints" => 7             
     ------------------------------------------------------------------------
     4, 5, 6}, {3}, {7}} => 1}},
                                
     ------------------------------------------------------------------------
     CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1}, {2,
                                    "NumberOfMarkedPoints" => 7             
     ------------------------------------------------------------------------
     4, 5, 7}, {3}, {6}} => 1}},
                                
     ------------------------------------------------------------------------
     CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1}, {2,
                                    "NumberOfMarkedPoints" => 7             
     ------------------------------------------------------------------------
     4, 6, 7}, {3}, {5}} => 1}},
                                
     ------------------------------------------------------------------------
     CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1}, {2,
                                    "NumberOfMarkedPoints" => 7             
     ------------------------------------------------------------------------
     5, 6, 7}, {3}, {4}} => 1}},
                                
     ------------------------------------------------------------------------
     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, 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},
                                    "NumberOfMarkedPoints" => 7            
     ------------------------------------------------------------------------
     {2, 3}, {4}, {5, 6}} => 1}},
                                 
     ------------------------------------------------------------------------
     CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 7},
                                    "NumberOfMarkedPoints" => 7
     ------------------------------------------------------------------------
     {2, 3}, {4, 5}, {6}} => 1}}}

o1 : List
Ways to use singletonSpineBasis :

singletonSpineBasis(ZZ)
For the programmer

The object singletonSpineBasis is a method function.