The integral chow ring of $M_2^{ct}$

This paper computes the integral Chow ring of the moduli space $M_2^{ct}$ of stable genus 2 curves of compact type. This is done by excising boundary strata from ${\bar{M}}_2$ one-by-one. During this process, we determine the Chow rings of all other open strata in ${\bar{M}}_2$ with $Z[1\mathrm{/}2]$-coefficients.