Essential normality for quotient modules and complex dimensions

Abstract

For analytic sets M˜ introduced in [9], we show that the corresponding quotient module Q of the Bergman module is p-essentially normal for all p>dimCM˜, which verifies the Geometric Arveson–Douglas Conjecture in this case. This result makes it possible to study the Helton–Howe trace invariants on both Q and the corresponding submodule R.