Classification of normal quartic surfaces with irrational singularities (Q1885111)

Normal quartic surfaces in \(\mathbb P^3\) with irrational singularities are classified by determining their minimal desingularization. Such a surface is determined by its minimal desingularization \(M\), the pullback \(D\) of a generic hyperplane section and a non-zero effective anti-canonical divisor \(E\) on the desingularization. Geometric constructions of all possible triplets \((M,D,E)\) are given.