English

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

Algebraic Geometry 2015-03-12 v1

Abstract

Let \phi: \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 \phi a quadro-quadric special briational transformation if \phi and \phi^{-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 \phi^{-1} is smooth, or (ii) Z is a hypersurface.

Cite

@article{arxiv.1503.03385,
  title  = {Quadro-quadric special birational transformations from projective spaces to smooth complete intersections},
  author = {Qifeng Li},
  journal= {arXiv preprint arXiv:1503.03385},
  year   = {2015}
}
R2 v1 2026-06-22T08:50:12.634Z