KeelRelationAmongCurves -- write the Keel relation among F curves based on the input lists

Synopsis

Usage:

KeelRelationAmongCurves(P)
Inputs:
- P, a list,
Outputs:
- C, an instance of the type CurveClassRepresentativeM0nbar,

Description

This function writes a Keel relation among curves. It is an expression supported on four F-curves that is equivalent to zero.

Specifically, let $P = I_1 \cup \cdots \cup I_5$ be a partition of $\{1,...,n\}$ into five nonempty subsets. Then this function returns the curve class representative $ F_{I_1,I_2,I_3,I_4 \cup I_5} + F_{I_1 \cup I_2, I_3,I_4,I_5} - F_{I_1, I_4, I_3, I_2 \cup I_5} - F_{I_1 \cup I_4, I_3, I_2, I_5}$.

i1 : C1=KeelRelationAmongCurves({{1},{2},{3},{4},{5}})

o1 = CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 2}, {3}, {4}, {5}} => 1 }}
                                                                   {{1, 4}, {2}, {3}, {5}} => -1
                                                                   {{1}, {2, 5}, {3}, {4}} => -1
                                                                   {{1}, {2}, {3}, {4, 5}} => 1
                                    "NumberOfMarkedPoints" => 5

o1 : CurveClassRepresentativeM0nbar

i2 : L={  };

i3 : C2=curveClassRepresentativeM0nbar(5,L);

i4 : isEquivalent(C1,C2)

o4 = true

Ways to use KeelRelationAmongCurves :

KeelRelationAmongCurves(List)

For the programmer

The object KeelRelationAmongCurves is a method function.