Nœther decomposition for birational maps

الأصل · EN

Let ϕ be a birational map of the complex projective plane. We know that ϕ can be written as a composition of automorphisms of P²C and the standard quadratic birational map σ. This writing, that is non-unique, is minimal if the number n(ϕ) of σ is as small as possible. We prove that if ϕ is of degree d≥ 2, then [d/ 2](ϕ)≤ 2(2d-1).