Automorphism groups of quartic del Pezzo surfaces (Q1125904)

The author completely determines the automorphism group of any quartic del Pezzo surface. More precisely, a quartic del Pezzo surface can be obtained by blowing up first the projective plane at four points in general position -- hence obtaining a quintic del Pezzo surface \(X\) -- and then blowing up again \(X\) at another point \(P\). The author describes the automorphism group of a quartic del Pezzo surface depending on the position of \(P\) in \(X\).