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

## 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 .