| Safe Haskell | None |
|---|---|
| Language | Haskell2010 |
Math.RootLoci.Dual.Restriction
Description
Formula for the dual cohomology class of the cones over the strata (sometimes called Thom polynomial)
in terms of the Chern classes c1 and c2, from the author's MSc thesis.
Note that the dual class agress with the lowest degree part of the CSM class.
See: Balazs Komuves: Thom Polynomials via Restriction Equations; MSc thesis, ELTE, 2003
Synopsis
- affineDualMSc :: Partition -> ZMod Chern
- projDegreeFromDual :: Int -> ZMod Chern -> Integer
- degreeMSc :: Partition -> Integer
- dualClassFromProjCSM :: forall base. ChernBase base => ZMod (Gam base) -> ZMod base
- dualClassFromAffCSM :: ChernBase base => ZMod base -> ZMod base
- lemma913 :: Partition -> Int -> Bool
- divideIntoTwo :: Partition -> Set (Partition, Partition)
- divideIntoTwoNonEmpty :: Partition -> Set (Partition, Partition)
The dual class
affineDualMSc :: Partition -> ZMod Chern Source #
The affine Thom polynomial formula from my MSc thesis
Degree
Arguments
| :: Int | number of points = dimension of the projective space |
| -> ZMod Chern | dual class |
| -> Integer | degree |
Compute the projective degree from the affine equivariant dual (which can be checked against Hilbert's formula)
This is just a simple substition:
alpha -> 1/n beta -> 1/n
or in terms of Chern classes:
c1 -> 2/n c2 -> 1/n^2
degreeMSc :: Partition -> Integer Source #
Compute the degree of the strata via the formula for the dual class
extract the dual class from the CSM class
dualClassFromProjCSM :: forall base. ChernBase base => ZMod (Gam base) -> ZMod base Source #
The dual class of the closure agress with the lowest degree part of the CSM class.
Lemma 9.1.3
lemma913 :: Partition -> Int -> Bool Source #
Checks if Lemma 9.1.3 from the thesis is true for the given inputs