| Safe Haskell | None |
|---|---|
| Language | Haskell2010 |
Math.RootLoci.Segre.Equivariant
Description
The equivariant Segre-Schwartz-MacPherson classes
We can recover the Segre-SM classes by dividing the CSM class by the total Chern class of the tangent bundle of the (smooth) ambient variety.
The Segre-SM class is useful because it behaves well wrt. pullback.
Synopsis
- affTotalChernClass :: ChernBase base => Int -> ZMod base
- affTotalChernClassByDegree :: ChernBase base => Int -> [ZMod base]
- recipTotalChernClass :: forall base. ChernBase base => Int -> [ZMod base]
- recipTotalChernClass2 :: forall base. ChernBase base => Int -> [ZMod base]
- recipTotalChernClassSlow :: forall base. ChernBase base => Int -> [ZMod base]
- divideByTotalChernClass :: ChernBase base => Int -> ZMod base -> [ZMod base]
- divideByTotalChernClassSlow :: ChernBase base => Int -> ZMod base -> [ZMod base]
- affineOpenSegreSM :: ChernBase base => Partition -> [ZMod base]
- affineZeroSegreSM :: ChernBase base => Int -> [ZMod base]
- affineClosedSegreSM :: ChernBase base => Partition -> [ZMod base]
The total Chern class
affTotalChernClass :: ChernBase base => Int -> ZMod base Source #
Total Chern class of the representation Sym^m C^2
c(Sym^m C^2) = \prod_{i=0}^m (1 + i*a + (m-i)*b)affTotalChernClassByDegree :: ChernBase base => Int -> [ZMod base] Source #
Parts of the total Chern class, separated by degree
Inverse of the total Chern class
recipTotalChernClass :: forall base. ChernBase base => Int -> [ZMod base] Source #
Infinite power series expansion (by degree) of the multiplicative
inverse of the total Chern class of the representation Sym^m C^2
This is just the sum of all complete symmetric polynomials of the sums.
recipTotalChernClass2 :: forall base. ChernBase base => Int -> [ZMod base] Source #
Another implementation of recipTotalChernClass
recipTotalChernClassSlow :: forall base. ChernBase base => Int -> [ZMod base] Source #
A third, very slow implementation of recipTotalChernClass
divideByTotalChernClass :: ChernBase base => Int -> ZMod base -> [ZMod base] Source #
Divides a polynomial with the total chern class. As the result is an infinite power series, we return it's homogeneous parts as an infinite list.
Equivalent (but should be faster than) to:
separeteGradedParts what `mulSeries` (recipTotalChernClass m)
divideByTotalChernClassSlow :: ChernBase base => Int -> ZMod base -> [ZMod base] Source #
Another, very slow implementation of divideByTotalChernClass
Affine Segre-SM classes
affineOpenSegreSM :: ChernBase base => Partition -> [ZMod base] Source #
Affine equivariant Segre-SM class of the open strata