“School of Mathematics”

Back to Papers Home
Back to Papers of School of Mathematics

Paper   IPM / M / 16145
School of Mathematics
  Title:   On the structure of the kappa-ring
1.  Eaman Eftekhary
2.  Iman Setayesh
  Status:   Published
  Journal: Int. Math. Res. Not.
  Vol.:  2017
  Year:  2017
  Pages:   3281-3321
  Supported by:  IPM
We obtain lower bounds on the rank of the kappa ring \kring of the Delign-Mumford compactification of the moduli space of curves in different degrees. For this purpose, we introduce a quotient κc*(\Mgnbar) of \kring, and show that the rank of this latter ring in degree d is bounded below by |\PP(d,3g−2+nd)| where \PP(d,r) denotes the set of partitions of the positive integer d into at most r parts. In codimension 1 (i.e. d=3g−4+n) we show that the rank of κc*(\Mgnbar) is equal to n−1 for g=1, and is equal to



for g > 1. Furthermore, in codimension e=3g−3+nd, the rank of κc*(\Mgnbar) (as g and e remain fixed and n grows large) is asymptotic to




Download TeX format
back to top
scroll left or right