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

Abstract

Let ϕ: \mathbb{P}^{r}\dashrightarrow Z be a birational transformation with a smooth connected base locus scheme, where Z\subseteq\mathbb{P}^{r+c} is a nondegenerate prime Fano manifold. We call ϕa quadro-quadric special briational transformation if ϕand ϕ^{-1} are defined by linear subsystems of |\mathcal{O}_{\mathbb{P}^{r}}(2)| and |\mathcal{O}_{Z}(2)| respectively. In this paper we classify quadro-quadric special birational transformations in the cases where either (i) Z is a complete intersection and the base locus scheme of ϕ^{-1} is smooth, or (ii) Z is a hypersurface.

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• On special quadratic birational transformations of a projective space into a hypersurface
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• Special birational transformations of projective spaces
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Cited by in corpus (1)

• Examples of special quadratic birational transformations into complete intersections of quadrics