Gebhard Martin, Automorphisms of del Pezzo Surfaces I

Motivated by the classification of finite subgroups of the Cremona group of the plane, I will survey old and new results on automorphism groups of del Pezzo surfaces. In particular, I will report on joint work with Igor Dolgachev on the classification of automorphism groups of smooth del Pezzo surfaces and on joint work with Claudia Stadlmayr on the classification of vector fields on mildly singular del Pezzo surfaces. Special emphasis will be placed on the theory of actions of infinitesimal group schemes and characteristic-free methods in classical algebraic geometry.