Special birational transformations of projective spaces

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.

Minor mistake in Theorem 7 corrected, references updated

References in corpus (1)

• Quadro-quadric special birational transformations of projective spaces

Cited by in corpus (3)

• Quadro-quadric special birational transformations of projective spaces
• Examples of special quadratic birational transformations into complete intersections of quadrics
• Quadro-quadric special birational transformations from projective spaces to smooth complete intersections