Mathematics Colloquia and Seminars

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We discuss the classical subject of smooth of degree d projective surfaces in the three dimensional space. In particular we will analyse smooth cubic surfaces. A classical theorem states that a smooth cubic surface contains 27 straight lines. These can be characterized independently of the embedding into projective space as the rational lines with self-intersection number −1. Moreover, a smooth cubic surface can also be described as a rational surface obtained by blowing up six points in the projective plane in general position, or a del Pezzo surfaces of degree 6. This is related to the Enriques classification of surfaces.