On the varieties of the second row of the split Freudenthal–Tits Magic Square
[Sur les variétés de la deuxième rangée du carré magique deployé de Freudenthal–Tits]
Annales de l'Institut Fourier, Tome 67 (2017) no. 6, pp. 2265-2305.

Le but principal de cet article est de fournir une caractérisation géométrique des analogues sur les corps quelconques des quatre variétés complexes de Severi, c’est-à-dire la surface de Veronese, la variété de Segre S(2,2), la grassmannienne G(2,6) et la variété exceptionnelle de type E 6 . Notre théorème peut être vu comme une généralisation considérable de l’approche de Mazzocca et Melone pour les surfaces de Veronese sur les corps finis. Cette approche utilise des analogues combinatoires de certaines propriétés, qui expriment que les variétés de Severi complexes sont lisses, comme axiomes.

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.

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DOI : https://doi.org/10.5802/aif.3136
Classification : 51E24,  51A45,  14M12,  17C37,  20G15
Mots clés : Variété de Severi, variété de Veronese, variété de Segre, grassmanniene, immeuble de Tits
@article{AIF_2017__67_6_2265_0,
     author = {Schillewaert, Jeroen and Van Maldeghem, Hendrik},
     title = {On the varieties of the second row of the split Freudenthal{\textendash}Tits Magic Square},
     journal = {Annales de l'Institut Fourier},
     pages = {2265--2305},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {67},
     number = {6},
     year = {2017},
     doi = {10.5802/aif.3136},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.3136/}
}
Schillewaert, Jeroen; Van Maldeghem, Hendrik. On the varieties of the second row of the split Freudenthal–Tits Magic Square. Annales de l'Institut Fourier, Tome 67 (2017) no. 6, pp. 2265-2305. doi : 10.5802/aif.3136. http://archive.numdam.org/articles/10.5802/aif.3136/

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