# kappa -- Miller-Morita-Mumford classes

• Usage:
kappa_a
• Inputs:
• Outputs:

## Description

This is an element in the ring created by hodgeRing. It is the Miller-Morita-Mumford class discussed in [AC].

Here is a simple example which calculates $\int_{{\bar M}_{1,1}} k_1$.

 i1 : R = hodgeRing (1, 1); i2 : kappa_1 o2 = kappa 1 o2 : R i3 : integral(1, 1, kappa_1) warning: clearing value of symbol tempCh to allow access to subscripted variables based on it : debug with expression debug 1257 or with command line option --debug 1257 1 o3 = -- 24 o3 : R

## References

[AC] Arbarello, E. and Cornalba, M. Combinatorial and algebro-geometric cohomology classes on the moduli spaces of curves. J. Algebraic Geom. 5. (1996), no. 4, 705--749.