Subelliptic estimates for the $\bar{\partial }$-problem on complex algebraic surfaces with isolated singularities

Abstract

We obtain subelliptic estimates for the $\bar{\partial }$-problem on complex algebraic surfaces embedded in ${\mathbb{C}}^n$ with isolated singularities. $W^{\epsilon }$ Sobolev norms of a form, $f$, for $0<\epsilon <1$ are estimated in terms of weighted $L^2$ norms of $\bar{\partial }f$ and ${\bar{\partial }}^{\ast }f$, with weights which vanish at the singularities, as well as weighted $L^2$ norms of $f$, with weights which blow up at the singularities.

14 pages. Comments welcome