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On the varieties of the second row of the split Freudenthal-Tits magic square

(2017) ANNALES DE L' INSTITUT FOURIER. 67(6). p.2265-2305
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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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Please use this url to cite or link to this publication:

Chicago
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.
APA
Schillewaert, Jeroen, & 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.
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.
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 67.6 (2017): 2265–2305. Print.
@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},
  isbn         = {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://dx.doi.org/10.5802/aif.3136},
  volume       = {67},
  year         = {2017},
}

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