Special birational transformations of projective spaces

Details Special birational transformations of projective spaces Special birational transformations of projective spaces

2012-03-26

arxiv.org/abs/1203.5690v1

Mathematics

Algebraic Geometry

First draft

Scientific paper

Extending some results of Crauder and Katz, and Ein and Shepherd-Barron on special Cremona transformations, we study birational transformations of the complex projective space 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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