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Paper
IPM / M / 16146 |
School of Mathematics
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Title: |
On the kappa ring of ―Mg,n
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Author(s): |
| 1. |
Eaman Eftekhary
| | 2. |
Iman Setayesh
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Status: |
Published
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Journal: |
Adv. Math.
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Vol.: |
298
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Year: |
2016
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Pages: |
89-121
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Supported by: |
IPM
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Abstract: |
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.
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