isToricDegeneration -- Does the matching field give rise to a toric degeneration

Usage:

result = isToricDegeneration L
Inputs:
- L, an instance of the type GrMatchingField or an instance of the type FlMatchingField,
Outputs:
- result, a Boolean value, does the matching field give rise to a toric degeneration

Description

A matching field is said to give rise to a toric degeneration (of the corresponding variety: Grassmannian or partial flag variety) if the matching field ideal is equal to the initial ideal of the Pluecker ideal with respect the weight order that induces the matching field. For further details on each of these ideals see the functions matchingFieldIdeal and plueckerIdeal.

i1 : L = diagonalMatchingField(2, 4)

o1 = Grassmannian Matching Field for Gr(2, 4)

o1 : GrMatchingField

i2 : I = plueckerIdeal L

o2 = ideal(p   p    - p   p    + p   p   )
            2,3 1,4    1,3 2,4    1,2 3,4

o2 : Ideal of QQ[p   ..p   , p   , p   , p   , p   ]
                  1,2   1,3   2,3   1,4   2,4   3,4

i3 : J = matchingFieldIdeal L

o3 = ideal(p   p    - p   p   )
            2,3 1,4    1,3 2,4

o3 : Ideal of QQ[p   ..p   , p   , p   , p   , p   ]
                  1,2   1,3   2,3   1,4   2,4   3,4

i4 : J == ideal leadTerm(1, I)

o4 = true

i5 : isToricDegeneration L

o5 = true

In the above example, the last two tests are the same.

If the matching field provided is not defined in terms of a weight matrix then one is automatically computed for it. If the matching field is not coherent then this will produce an error.

A note of caution. While this function takes any object of type MatchingField, the function will produce an error if the supplied object is not of type GrMatchingField or FlMatchingField.

Ways to use isToricDegeneration:

isToricDegeneration(MatchingField)

For the programmer

The object isToricDegeneration is a method function.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/MatchingFields.m2:1961:0.

isToricDegeneration -- Does the matching field give rise to a toric degeneration

Description

See also

Menu

Ways to use isToricDegeneration:

For the programmer