Topics on $K3$ surfaces - Lecture 3: Basic properties of $K3$ surfaces
Apparaît dans la collection : Complex geometry: a modern viewpoint / Géométrie complexe : un point de vue moderne
Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space. The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire. The topics of the lecture are the following:
² $K3$ surfaces in the Enriques-Kodaira classification. ² Examples; Kummer surfaces. ² Basic properties of $K3$ surfaces; Torelli theorem and surjectivity of the period map. ² The study of automorphisms on $K3$ surfaces: basic facts, examples. ² Symplectic automorphisms of $K3$ surfaces, classification, moduli spaces.
