Safe Haskell | None |
---|---|
Language | Haskell2010 |
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.
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