15-nodal quartic surfaces. II: The automorphism group (Q2657369)

A quartic surface in the complex projective \(3\)-dimensional space that has exactly \(16\) ordinary double points as its only singularities it is called a Kummer surface. Kummer surfaces have been much investigated. The authors of this paper consider quartic surfaces \(X_n\) in the complex projective \(3\)-dimensional space with \(n<16\) ordinary double points, focusing on those quartics that satisfy a given list of conditions. The first of these condition is that \(X_n\) ``can be degenerated by acquiring \(16-n\) nodes and hence becomes isomophic to a Kummer surface''. A general minimal resolution \(Y_{15}\) of a quartic \(X_{15}\) satisfies all the required conditions. The authors compute the birational automorphism group \(\mathrm{Aut}(Y_{15})\). They describe a set of generators and defining relations. The applied method requires explicit computations that the authors made by using GAP.