Quadro-quadric cremona transformations in low dimensions via the JC-correspondence

Luc Pirio (1) , Francesco Russo (2, 3)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 MATHRISK - Mathematical Risk handling
3 OC - Optimisation et commande

We apply the results of arXiv:1109.3573 to study quadro-quadric Cremona transformations in low-dimensional projective spaces. In particular we describe new very simple families of such birational maps and obtain complete and explicit classifications in dimension four and five.

Keywords: Jordan algebra; Cremona transformation

Domains: Mathematics [math]; Algebraic Geometry [math.AG]

Luc Pirio, Francesco Russo. Quadro-quadric cremona transformations in low dimensions via the JC-correspondence. Annales de l'Institut Fourier, 2014, 64 (1), pp.71-111. ⟨10.5802/aif.2839⟩. ⟨hal-00709666⟩