Geometirc Arveson-Douglas Conjecture - Decomposition of Varieties

Abstract

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 Suárez, 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 ${\mathbb{B}}_n$.

25 pages