We study real birational transformations of the real projective plane which are diffeomorphisms. It turns out that their degree must be congruent to 1 mod 4, and that they are generated by linear automorphisms and transformations of degree 5 centred at 3 pairs of conjugated imaginary points. Our approach is inspired by recent proofs of the classical theorem of Noether and Castelnuovo that use the Sarkisov program.
Cite this article
Thierry Vust, Felice Ronga, Diffeomorfismi birazionali del piano proiettivo reale. Comment. Math. Helv. 80 (2005), no. 3, pp. 517–540DOI 10.4171/CMH/24