Classification of simple quartics up to equisingular deformation (Q2357392)

A simple quartic is a surface in \(\mathbb{P}^3_{\mathbb{C}}\) of degree \(4\) with only A-D-E type singularities. Two such quartics are said to be equisingular deformation equivalent if they belong to the same deformation family with constant Milnor number A simple quartic \(X\subset \mathbb{P}^3_{\mathbb{C}}\) is non-special iff \(H_1(X\setminus(\mathrm{sing}(x)\cup H))=0\), where \(\mathrm{sing}(X)\) is the singular locus of \(X\) and \(H\) is a generic hyperplane section of \(X\). A complete equisingular deformation classification of non-special simple quartic surfaces is given.