Special birational transformations of projective spaces

Extending some results of Crauder and Katz, and Ein and Shepherd-Barron on special Cremona transformations, we study birational transformations of Pr onto a prime Fano manifold such that the base locus X⊂Pr is smooth irreducible and reduced. The main results are a complete classification when X has...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2016-02, Vol.289, p.567-602
Main Authors: Alzati, Alberto, Sierra, José Carlos
Format: Article
Language:English
Subjects:
Cremona transformations
Fano manifolds
Special birational transformations
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Summary:Extending some results of Crauder and Katz, and Ein and Shepherd-Barron on special Cremona transformations, we study birational transformations of Pr onto a prime Fano manifold such that the base locus X⊂Pr is smooth irreducible and reduced. The main results are a complete classification when X has either dimension 1 and 2, or codimension 2. Partial results are also obtained when X has dimension 3.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2015.11.018