Quadro-quadric special birational transformations of projective spaces
| Autor: | Alzati, Alberto, Sierra, José Carlos |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Int. Math. Res. Notices (2013) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1093/imrn/rnt173 |
| Popis: | Special birational transformations $\Phi:\p^r\da Z$ defined by quadric hypersurfaces are studied by means of the variety of lines $\mathcal L_z\subset\p^{r-1}$ passing through a general point $z\in Z$. Classification results are obtained when $Z$ is either a Grassmannian of lines, or the 10-dimensional spinor variety, or the $E_6$-variety. In the particular case of quadro-quadric transformations, we extend the well-known classification of Ein and Shepherd-Barron coming from Zak's classification of Severi varieties to a wider class of prime Fano manifolds $Z$. Combining both results, we get a classification of special birational transformations $\Phi:\p^r\da Z$ defined by quadric hypersurfaces onto (a linear setion of) a rational homogeneous variety different from a projective space and a quadric hypersurface. Comment: First draft |
| Databáze: | arXiv |
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