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Shedule -


Introduction to real del Pezzo surfaces

Salle Grisvard

Del Pezzo surfaces are algebraic surfaces playing an important role in the classification of algebraic projective surfaces up to birational transformations. Over C, a smooth del Pezzo surface of degree d is either isomorphic to P2C (d = 9) or to P1C × P1C (d = 8) or to the blow-up of P2C in 1 ≤ r ≤ 8 points in general position, where d = 9 − r. Before explaining the terminology, we will first see how algebraic projective varieties defined over a perfect field (e.g. R later on) naturally arise while studying some fibrations over P1C, motivating the interest in the classification of smooth (rational) del Pezzo surfaces over a perfect field. We will then introduce the notions of real structures and real forms of complex projective surfaces, and we will see that there are exactly two non-equivalent rational real models of P1C ×P1C. Finally, we will present the classification of smooth real rational del Pezzo surfaces of degree 6, that were initially introduced over C to be the blow-up of P2C in three points in general position.