Special birational transformations of projective spaces

2012/03/26 by Alberto Alzati, Alzati, Alberto, José Carlos Sierra +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1203.5690

openalex publication_date 2012/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Abstract

Extending some results of Crauder and Katz, and Ein and Shepherd-Barron on special Cremona transformations, we study birational transformations of the complex projective spaces onto prime Fano manifolds such that the base locus X of the transformations is smooth, irreducible and reduced. We get a complete classification when X has dimension 1, or dimension 2, or codimension 2. We also get partial results when X has dimension 3.

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