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.
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