All links are semiholomorphic

Semiholomorphic polynomials are functions $f:{\mathbb{C}}^2\to \mathbb{C}$ that can be written as polynomials in complex variables $u$, $v$ and the complex conjugate $\bar{v}$. We prove the semiholomorphic analogoue of Akbulut’s and King’s “All knots are algebraic”, that is, every link type in the 3-sphere arises as the link of a weakly isolated singularity of a semiholomorphic polynomial. Our proof is constructive, which allows us to obtain an upper bound on the polynomial degree of the constructed functions.