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

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