# ag.algebraic geometry – Cubic surface in \$mathbb{P}^3\$ with isolated singularities and generic fiber

I was trying to read the paper “Hypersurfaces complements, Alexander Modules and Monodromy” by Dimca and Nemethi. In example 3.4. they mentioned a cubic surface $$V$$ in $$mathbb{P}^3$$ having two singularities of type $$A_1$$ and $$A_5$$ and they took $$H$$, a generic plane so that $$X=V-H$$ becomes singular. In this case, they also mentioned that the associated polynomial $$f$$ is tame.

Now my question is as follows: Is $$X$$ the generic fiber of a polynomial? If so how to recover such a polynomial?