Special birational transformations Graphic defined by quadric hypersurfaces are studied by means of the variety of lines Graphic passing through a general point z∈Z. Classification results are obtained when Z is either a Grassmannian of lines, or the 10-dimensional spinor variety, or the E6-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 Graphic defined by quadric hypersurfaces onto (a linear section of) a rational homogeneous variety different from a projective space and a quadric hypersurface.
Quadro-quadric special birational transformations of projective spaces / A. Alzati, J.C. Sierra. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - 2015:1(2015), pp. 55-77. [10.1093/imrn/rnt173]
Quadro-quadric special birational transformations of projective spaces
A. AlzatiPrimo
;
2015
Abstract
Special birational transformations Graphic defined by quadric hypersurfaces are studied by means of the variety of lines Graphic passing through a general point z∈Z. Classification results are obtained when Z is either a Grassmannian of lines, or the 10-dimensional spinor variety, or the E6-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 Graphic defined by quadric hypersurfaces onto (a linear section of) a rational homogeneous variety different from a projective space and a quadric hypersurface.File | Dimensione | Formato | |
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