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}
}