Let $\Delta:Y\rightarrow X$ a closed immersion of $k$schemes of finite type and equidimensionnal.
We assume that $\Delta^{*}[d]IC_{X}=IC_{Y}$, if $X$ is CohenMacaulay, does it imply that $Y$ is CohenMacaulay?
Let $\Delta:Y\rightarrow X$ a closed immersion of $k$schemes of finite type and equidimensionnal. We assume that $\Delta^{*}[d]IC_{X}=IC_{Y}$, if $X$ is CohenMacaulay, does it imply that $Y$ is CohenMacaulay? 

