Invariants of Surfaces of Degree $d$ in ${\mathbb{P}}^n$

We prove that several invariants of a possibly singular complex affine or projective variety of degree $d$ in the affine space ${\mathbb{A}}^n$, or ${\mathbb{P}}^n$, are bounded by a function of $d$ alone, provided $b_1=0$ for a resolution of singularities of the variety.