Extending some results of Crauder and Katz and Ein and Sheperd-Barron on special Cremona transformations, we study birational transformations of P^r onto a prima Fano manifold such that the base locus X in P^r 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.
Special birational transformations of projective spaces / A. Alzati, J.C. Sierra. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - 289(2016 Feb), pp. 567-602. [10.1016/j.aim.2015.11.018]
Special birational transformations of projective spaces
A. AlzatiPrimo
;
2016
Abstract
Extending some results of Crauder and Katz and Ein and Sheperd-Barron on special Cremona transformations, we study birational transformations of P^r onto a prima Fano manifold such that the base locus X in P^r 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.
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