coincident-root-loci-0.2: Equivariant CSM classes of coincident root loci

Math.RootLoci.CSM.Equivariant.Recursive

Contents

Description

We compute the GL2-equivariant open and closed CSM classes recursively, starting from smallest strata.

The idea is that we have a smooth resolution of the closure of the strata X_mu, namely, the set of n=length(mu) ordered points: Q^n = P^1 x ... x P^1

We can pushforward this to Q^m, and get a linear combination of the strata of the CSM-s we want to compute. Since the smallest strata is actually closed, we know that, and can work upward from that.

This is rather slow, however as it's a very different algorithm copmared to the direct approach, it's useful for checking if the two agrees.

Synopsis

# CSM calculation

upperClass :: ChernBase base => SetPartition -> ZMod (Eta base) Source #

This is just the pushforward along Delta_nu of the tangent Chern class.

As Delta is injective, the resulting class is just the CSM class of the closed ordered strata corresponding to one of the set partitions which matches the given partition

lowerClass :: ChernBase base => Partition -> ZMod (Gam base) Source #

pushforward of upperCSM to the space of unordered points

openCSM :: ChernBase base => Partition -> ZMod (Gam base) Source #

We know from the pushforward property of CSM clsses that (pi_* upperCSM) = sum (chi * openCSM). we can use this to recursively compute the CSM classes of the open loci

closedCSM :: ChernBase base => Partition -> ZMod (Gam base) Source #

To compute the CSM of the closed loci, we just some over the open strata in the closure.