  In this paper, we prove the Geometric Arveson-Douglas Conjecture for a
special case which allow some singularity on $\partial{\mathbb{B}_n}$. More
precisely, we show that if a variety can be decomposed into two varieties, each
having nice properties and intersecting nicely with $\partial\mathbb{B}_n$,
then the Geometric Arveson-Douglas Conjecture holds on this variety. We obtain
this result by applying a result by Su\'arez, which allows us to "localize" the
problem. Our result then follows from the simple case when the two varieties
are intersection of linear subspaces with $\mathbb{B}_n$.
