Quadro-quadric special birational transformations from projective spaces to smooth complete intersections

2015/03/11 by Qifeng Li, Li, Qifeng
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1503.03385

openalex publication_date 2015/03/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let ϕ: ℙ^r\dashrightarrow Z be a birational transformation with a smooth connected base locus scheme, where Z⊆ℙ^r+c is a nondegenerate prime Fano manifold. We call ϕa quadro-quadric special briational transformation if ϕand ϕ^-1 are defined by linear subsystems of |O_ℙ^r(2)| and |O_Z(2)| respectively. In this paper we classify quadro-quadric special birational transformations in the cases where either (i) Z is a complete intersection and the base locus scheme of ϕ^-1 is smooth, or (ii) Z is a hypersurface.

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