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“School of Mathematics”

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Paper   IPM / M / 16146
School of Mathematics
  Title:   On the kappa ring of Mg,n
  Author(s): 
1.  Eaman Eftekhary
2.  Iman Setayesh
  Status:   Published
  Journal: Adv. Math.
  Vol.:  298
  Year:  2016
  Pages:   89-121
  Supported by:  IPM
  Abstract:
Let κe(\Mgnbar) denote the kappa ring of \Mgnbar in codimension e (equivalently, in degree d=3g−3+ne). 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

n+e
e


g+e
e


(e+1)!

g+e
e

ne

e!(e+1)!
.
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 κnd(\Mbar1,n) is equal to |\PP1(d,nd)|, 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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