  The lens space $L_{p,q}$ is the orbit space of a $\mathbb{Z}_{p}$-action on
the three sphere. We investigate polynomials of two complex variables that are
invariant under this action, and thus define links in $L_{p,q}$. We study
properties of these links, and their relationship with the classical algebraic
links. We prove that all algebraic links in lens spaces are fibered, and obtain
results about their Seifert genus. We find some examples of algebraic knots in
lens spaces, whose lift in the $3$-sphere is a torus link.
