coincident-root-loci-0.3: Equivariant CSM classes of coincident root loci
Safe HaskellNone
LanguageHaskell2010

Math.RootLoci.CSM.Projective

Description

Compute the non-equivariant CSM in P^n recursively

Synopsis

Pushforwards

delta_star :: Partition -> ZMod US -> ZMod HS Source #

A group generator on the left is a subset (=product) of U-s, which we map to a linear combinaton of H-s. This is then extended additively to the cohomology ring.

pi_star Source #

Arguments

:: Int

the number of points m (with multiplicity)

-> ZMod HS

the cohomoly class "up"

-> ZMod G 

The pushforward map pi_* along pi.

A (cohomology) group generator above is a subset (=product) of H-s, which we map to a group generator below. This defines the map on the cohomology ring by additive extension.

Easy things

tangentChernClass :: Int -> ZMod US Source #

The total Chern class of the tangent bundle of Q^d = P^1 x P^1 x ... x P^1

This is just the product of (1+2u_i)-s for i=[1..d]

smallestOrbitCSM :: Int -> ZMod G Source #

The CSM of the smallest orbit: 1 point with multiplicity n, which is just the rational normal curve in P^n.

CSM calculation

upperCSM :: Partition -> ZMod HS Source #

We know that:

csm(im(Delta) = Delta_* c(TQ^d)
c(TQ^d) = (1+2*u1) (1+2*u2) ... (1+2*ud)

From these, we can compute csm(im(Delta_nu)) recursively

lowerCSM :: Partition -> ZMod G Source #

A formula for pi_*(csm(im(delta))). This should satisfy

lowerCSM part = pi_star n (upperCSM part)

openCSM :: Partition -> ZMod G Source #

Cached CSM computation of the open strata

closedCSM :: Partition -> ZMod G Source #

To get the CSM of the closed strata, we just sum over the open strata contained in the closure.

extracting coefficients