Nœther decomposition for birational maps

2013/03/13 by Julie Déserti, Déserti, Julie
Mathematics · #14E07 #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #math.AG #math.GR #msc:14E07

paper · pdf · doi:10.48550/arxiv.1303.3120

This paper has been withdrawn by the author due to an error in the upper bound

arxiv created 2014/05/08 · arxiv updated 2014/05/12

Abstract

Let ϕ be a birational map of the complex projective plane. We know that ϕ can be written as a composition of automorphisms of ℙ²_ℂ and the standard quadratic birational map σ. This writing, that is non-unique, is minimal if the number \mathfrakn(ϕ) of σ is as small as possible. We prove that if ϕ is of degree d≥ 2, then [(ln d)/(ln 2)]≤\mathfrakn(ϕ)≤ 2(2d-1).

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