On the varieties of the second row of the split Freudenthal-Tits magic square
- Author
- Jeroen Schillewaert and Hendrik Van Maldeghem (UGent)
- Organization
- Abstract
- Our main aim is to provide a uniform geometric characterization of the analogues over arbitrary fields of the four complex Severi varieties, i.e. the quadric Veronese varieties in 5-dimensional projective spaces, the Segre varieties in 8-dimensional projective spaces, the line Grassmannians in 14-dimensional projective spaces, and the exceptional varieties of type E-6 in 26-dimensional projective space. Our theorem can be regarded as a far-reaching generalization of Mazzocca and Melone's approach to finite quadric Veronesean varieties. This approach uses combinatorial analogues of smoothness properties of complex Severi varieties as axioms.
- Keywords
- SEVERI VARIETIES, VERONESEAN CAPS, GEOMETRIES, EMBEDDINGS, MANIFOLDS, CURVES, PLANES, SPACES, Severi variety, Veronese variety, Segre variety, Grassmann variety, Tits-building
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8566695
- MLA
- Schillewaert, Jeroen, and Hendrik Van Maldeghem. “On the Varieties of the Second Row of the Split Freudenthal-Tits Magic Square.” ANNALES DE L’ INSTITUT FOURIER, vol. 67, no. 6, 2017, pp. 2265–305, doi:10.5802/aif.3136.
- APA
- Schillewaert, J., & Van Maldeghem, H. (2017). On the varieties of the second row of the split Freudenthal-Tits magic square. ANNALES DE L’ INSTITUT FOURIER, 67(6), 2265–2305. https://doi.org/10.5802/aif.3136
- Chicago author-date
- Schillewaert, Jeroen, and Hendrik Van Maldeghem. 2017. “On the Varieties of the Second Row of the Split Freudenthal-Tits Magic Square.” ANNALES DE L’ INSTITUT FOURIER 67 (6): 2265–2305. https://doi.org/10.5802/aif.3136.
- Chicago author-date (all authors)
- Schillewaert, Jeroen, and Hendrik Van Maldeghem. 2017. “On the Varieties of the Second Row of the Split Freudenthal-Tits Magic Square.” ANNALES DE L’ INSTITUT FOURIER 67 (6): 2265–2305. doi:10.5802/aif.3136.
- Vancouver
- 1.Schillewaert J, Van Maldeghem H. On the varieties of the second row of the split Freudenthal-Tits magic square. ANNALES DE L’ INSTITUT FOURIER. 2017;67(6):2265–305.
- IEEE
- [1]J. Schillewaert and H. Van Maldeghem, “On the varieties of the second row of the split Freudenthal-Tits magic square,” ANNALES DE L’ INSTITUT FOURIER, vol. 67, no. 6, pp. 2265–2305, 2017.
@article{8566695,
abstract = {{Our main aim is to provide a uniform geometric characterization of the analogues over arbitrary fields of the four complex Severi varieties, i.e. the quadric Veronese varieties in 5-dimensional projective spaces, the Segre varieties in 8-dimensional projective spaces, the line Grassmannians in 14-dimensional projective spaces, and the exceptional varieties of type E-6 in 26-dimensional projective space. Our theorem can be regarded as a far-reaching generalization of Mazzocca and Melone's approach to finite quadric Veronesean varieties. This approach uses combinatorial analogues of smoothness properties of complex Severi varieties as axioms.}},
author = {{Schillewaert, Jeroen and Van Maldeghem, Hendrik}},
issn = {{0373-0956}},
journal = {{ANNALES DE L' INSTITUT FOURIER}},
keywords = {{SEVERI VARIETIES,VERONESEAN CAPS,GEOMETRIES,EMBEDDINGS,MANIFOLDS,CURVES,PLANES,SPACES,Severi variety,Veronese variety,Segre variety,Grassmann variety,Tits-building}},
language = {{eng}},
number = {{6}},
pages = {{2265--2305}},
title = {{On the varieties of the second row of the split Freudenthal-Tits magic square}},
url = {{http://doi.org/10.5802/aif.3136}},
volume = {{67}},
year = {{2017}},
}
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