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 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.
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 , la grassmannienne et la variété exceptionnelle de type . 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.
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Keywords: Severi variety, Veronese variety, Segre variety, Grassmann variety, Tits-building
Mot clés : Variété de Severi, variété de Veronese, variété de Segre, grassmanniene, immeuble de Tits
Schillewaert, Jeroen 1; Van Maldeghem, Hendrik 2
@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 = {https://aif.centre-mersenne.org/articles/10.5802/aif.3136/} }
TY - JOUR AU - Schillewaert, Jeroen AU - Van Maldeghem, Hendrik TI - On the varieties of the second row of the split Freudenthal–Tits Magic Square JO - Annales de l'Institut Fourier PY - 2017 SP - 2265 EP - 2305 VL - 67 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3136/ DO - 10.5802/aif.3136 LA - en ID - AIF_2017__67_6_2265_0 ER -
%0 Journal Article %A Schillewaert, Jeroen %A Van Maldeghem, Hendrik %T On the varieties of the second row of the split Freudenthal–Tits Magic Square %J Annales de l'Institut Fourier %D 2017 %P 2265-2305 %V 67 %N 6 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3136/ %R 10.5802/aif.3136 %G en %F AIF_2017__67_6_2265_0
Schillewaert, Jeroen; Van Maldeghem, Hendrik. On the varieties of the second row of the split Freudenthal–Tits Magic Square. Annales de l'Institut Fourier, Volume 67 (2017) no. 6, pp. 2265-2305. doi : 10.5802/aif.3136. https://aif.centre-mersenne.org/articles/10.5802/aif.3136/
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