Flows of birational quadratic transformations in the complex projective space of dimension 3

2010/02/18 by Mònica Manjarín, Monica Manjarin, Manjarin, Monica
Mathematics · #14E05 #14E07 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematics and Applications #advanced mathematical theories #math.AG #msc:14E05 #msc:14E07

paper · pdf · doi:10.48550/arxiv.1002.3466

35 pages

arxiv created 2010/02/18 · openalex publication_date 2010/02/18 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study and classify up to a linear conjugation germs of flows in the space of quadratic birational transformations of the complex projective space of dimension 3. As a consequence we show that every quadratic flow preserves a pencil of planes through a line.

Related

• On special quadratic birational transformations of a projective space
• Birational transformations belonging to Galois points for a certain plane quartic
• Quadro-quadric special birational transformations from projective spaces to smooth complete intersections
• The cubo-cubic transformation of the smooth quadric fourfold is very special
• Generalised Manin transformations and QRT maps