We are interested in the following problem: Given the germ of a meromorphic function $F$ (holomorphic foliation $\mathcal{F}$) on $(\mathbb{C}^2,0)$, does there exist an algebraic surface $S$, a point $p\in S$ and a rational function (resp. algebraic foliation) on $S$ such that $F$ (resp. $\mathcal{F}$) is the germ of this rational function (resp. algebraic foliation) around $p$? We call such germs algebraizable.

In this talk we will address this question and see some cases in which we can guarantee that certain germs are algebraizable. We will also construct what we believe to be the first concrete example of a non-algebraizable germ of a singular foliation on $(\mathbb{C}^2,0)$.