M0nbar -- calculations for divisors and curves on the moduli space of stable n-pointed genus zero curves

Description

This package contains two types for working with divisor classes and curve classes on $\bar{M}_{0,n}$, the moduli space of stable n-pointed genus zero curves. The basic types are DivisorClassRepresentativeM0nbar and CurveClassRepresentativeM0nbar.

i1 : L1= { {{{2,1},{3},{4},{5}},-2}, {{{1,3},{2},{4},{5}},-7}, {{{1,4},{2},{3},{5}},1}};

i2 : C=curveClassRepresentativeM0nbar(5,L1);

i3 : L2=new HashTable from { {{1,3},1}, {{1,4},1}};

i4 : D=divisorClassRepresentativeM0nbar(5,L2);

i5 : intersection(C,D)

o5 = 6

Authors

Han-Bom Moon <hmoon8@fordham.edu>
Dave Swinarski <dswinarski@fordham.edu>

Version

This documentation describes version 0.3 of M0nbar.

Source code

The source code from which this documentation is derived is in the file M0nbar.m2.

Exports

Types
- CurveClassRepresentativeM0nbar -- class implementing curves on the moduli space of stable n-pointed genus zero curves
- DivisorClassRepresentativeM0nbar -- class implementing divisors on the moduli space of stable n-pointed genus zero curves
Functions and commands
- curveClassRepresentativeM0nbar -- creates an object of type CurveClassRepresentativeM0nbar
- divisorClassRepresentativeM0nbar -- creates an object of type DivisorClassRepresentativeM0nbar
- Fcurves -- lists the F-curves for a given n
- FcurvesOfGivenShape -- a list of the F-curves with the given shape
- intersection -- intersection number of a curve class and divisor class
- isEffectiveExpression -- determines whether a curve class expression is effective
- isEquivalent -- check whether two curve class representatives are numerically equivalent
- KeelRelationAmongCurves -- write the Keel relation among F curves based on the input lists
- negativeSum -- sum of the negative coefficients in CurveClassRepresentativeM0nbar
- nonadjacentBasis -- computes the nonadjacent basis of divisors on M0nbar
- permute -- compute the image of a curve class representative under a permutation of the marked points
- seekEffectiveExpression -- seeks to write a curve class as an effective sum of F-curves
- singletonSpineBasis -- computes the singleton spine basis of curves on M0nbar
- writeCurveInDualNonadjacentBasis -- write a curve in the basis dual to the nonadjacent basis
- writeCurveInSingletonSpineBasis -- write a curve class in the singleton spine basis of curve
- writeDivisorInNonadjacentBasis -- write a divisor in the nonadjacent basis
Methods
- "curveClassRepresentativeM0nbar(ZZ,List)" -- see curveClassRepresentativeM0nbar -- creates an object of type CurveClassRepresentativeM0nbar
- CurveClassRepresentativeM0nbar + CurveClassRepresentativeM0nbar -- add two curve class representatives on M0nbar
- CurveClassRepresentativeM0nbar - CurveClassRepresentativeM0nbar -- subtract two curve class representatives on M0nbar
- curveClassRepresentativeM0nbar(ZZ,HashTable) -- creates an object of type CurveClassRepresentativeM0nbar
- "divisorClassRepresentativeM0nbar(ZZ,List)" -- see divisorClassRepresentativeM0nbar -- creates an object of type DivisorClassRepresentativeM0nbar
- DivisorClassRepresentativeM0nbar + DivisorClassRepresentativeM0nbar -- add two divisor class representatives on M0nbar
- DivisorClassRepresentativeM0nbar - DivisorClassRepresentativeM0nbar -- subtract two divisor class representatives on M0nbar
- divisorClassRepresentativeM0nbar(ZZ,HashTable) -- creates an object of type DivisorClassRepresentativeM0nbar
- "Fcurves(ZZ)" -- see Fcurves -- lists the F-curves for a given n
- "FcurvesOfGivenShape(ZZ,ZZ,ZZ,ZZ)" -- see FcurvesOfGivenShape -- a list of the F-curves with the given shape
- "intersection(CurveClassRepresentativeM0nbar,DivisorClassRepresentativeM0nbar)" -- see intersection -- intersection number of a curve class and divisor class
- intersection(DivisorClassRepresentativeM0nbar,CurveClassRepresentativeM0nbar) -- intersection number of a divisor class and curve class
- "isEffectiveExpression(CurveClassRepresentativeM0nbar)" -- see isEffectiveExpression -- determines whether a curve class expression is effective
- isEffectiveExpression(DivisorClassRepresentativeM0nbar) -- determines whether a divisor class expression is effective
- "isEquivalent(CurveClassRepresentativeM0nbar,CurveClassRepresentativeM0nbar)" -- see isEquivalent -- check whether two curve class representatives are numerically equivalent
- isEquivalent(DivisorClassRepresentativeM0nbar,DivisorClassRepresentativeM0nbar) -- check whether two divisor class representatives are numerically equivalent
- "KeelRelationAmongCurves(List)" -- see KeelRelationAmongCurves -- write the Keel relation among F curves based on the input lists
- "negativeSum(CurveClassRepresentativeM0nbar)" -- see negativeSum -- sum of the negative coefficients in CurveClassRepresentativeM0nbar
- "nonadjacentBasis(ZZ)" -- see nonadjacentBasis -- computes the nonadjacent basis of divisors on M0nbar
- Number * CurveClassRepresentativeM0nbar -- multiply a curve class representatives on M0nbar by a scalar
- Number * DivisorClassRepresentativeM0nbar -- multiply a divisor class representatives on M0nbar by a scalar
- "permute(List,CurveClassRepresentativeM0nbar)" -- see permute -- compute the image of a curve class representative under a permutation of the marked points
- permute(List,DivisorClassRepresentativeM0nbar) -- compute the image of a divisor class representative under a permutation of the marked points
- "seekEffectiveExpression(CurveClassRepresentativeM0nbar)" -- see seekEffectiveExpression -- seeks to write a curve class as an effective sum of F-curves
- "singletonSpineBasis(ZZ)" -- see singletonSpineBasis -- computes the singleton spine basis of curves on M0nbar
- tex(CurveClassRepresentativeM0nbar) -- convert to TeX format
- tex(DivisorClassRepresentativeM0nbar) -- convert to TeX format
- "writeCurveInDualNonadjacentBasis(CurveClassRepresentativeM0nbar)" -- see writeCurveInDualNonadjacentBasis -- write a curve in the basis dual to the nonadjacent basis
- "writeCurveInSingletonSpineBasis(CurveClassRepresentativeM0nbar)" -- see writeCurveInSingletonSpineBasis -- write a curve class in the singleton spine basis of curve
- writeCurveInSingletonSpineBasis(ZZ,List) -- write a curve class in the singleton spine basis of curve
- "writeDivisorInNonadjacentBasis(DivisorClassRepresentativeM0nbar)" -- see writeDivisorInNonadjacentBasis -- write a divisor in the nonadjacent basis

For the programmer

The object M0nbar is a package.