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Rendiconti del Circolo Matematico di Palermo

, Volume 61, Issue 3, pp 403–429 | Cite as

On special quadratic birational transformations of a projective space into a hypersurface

  • Giovanni Staglianò
Article

Abstract

We study transformations as in the title with emphasis on those having smooth connected base locus, called “special”. In particular, we classify all special quadratic birational maps into a quadric hypersurface whose inverse is given by quadratic forms by showing that there are only four examples having general hyperplane sections of Severi varieties as base loci.

Keywords

Birational transformation Base locus Quadric hypersurface Entry locus Tangential projection 

Mathematics Subject Classification (2000)

14E05 14N05 

Notes

Acknowledgments

The author wishes to thank Prof. Francesco Russo for his indispensable suggestions about the topics in this paper.

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Copyright information

© Springer-Verlag Italia 2012

Authors and Affiliations

  1. 1.Department of Mathematics and Computer SciencesUniversity of Study of CataniaCataniaItaly

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