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

Abstract

Let [Formula: see text] a birational transformation with a smooth connected base locus scheme, where [Formula: see text] is a nondegenerate prime Fano manifold covered by lines. We call [Formula: see text] a quadro-quadric special briational transformation if [Formula: see text] and [Formula: see text] are defined by linear subsystems of [Formula: see text] and [Formula: see text] respectively. In this paper, we classify quadro-quadric special birational transformations in the cases where either (i) [Formula: see text] is a complete intersection and the base locus scheme of [Formula: see text] is smooth, or (ii) [Formula: see text] is a hypersurface.