Seminar Algebra and Geometry: Maria Fernanda Robayo (Universität Basel)

Prime-order birational diffeomorphisms of the sphere

A birational diffeomorphism of a real projective algebraic variety X is a birational map that restricts to a diffeomorphism on the real points of X. In my talk, X will be the sphere, that is, the projective algebraic surface defined by x²+y²+z²=w² in P³_R endowed with the complex conjugation, which gives it its real structure. The systematic investigation of real algebraic surfaces has already begun with Comessatti in 1912. On the other hand, their automorphisms, the birational diffeomorphisms, have not been classified up to now. I will give an introduction into the subject and present the complete classification of birational diffeomorphisms of the sphere of prime order.

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