Let κe(\Mgnbar) denote the kappa ring of \Mgnbar in codimension e
(equivalently, in degree d=3g−3+n−e). For g,e ≥ 0 fixed, as the number n of the
markings grows large we show that the
rank of κe(\Mgnbar) is asymptotic to
When g ≤ 2 we show that a kappa class κ ∈ \kring is trivial if and only if
the integral of κ against all boundary strata is trivial.
For g=1 we further show that
the rank of κn−d(\Mbar1,n)
is equal to |\PP1(d,n−d)|, where
\PPi(d,k) denotes the set of partitions \p = (p1,...,pl) of d
such that at most k of the numbers p1,...,pl are greater than i.
Download TeX format
|
