Let be a Segre variety that is an -fold direct product of projective lines of size three. Given two geometric hyperplanes and of , let us call the triple the Veldkamp line of . We shall demonstrate, for the sequence , that the properties of geometric hyperplanes of are fully encoded in the properties of Veldkamp lines of . Using this property, a complete classification of all types of geometric hyperplanes of is provided. Employing the fact that, for , the (ordinary part of) Veldkamp space of is , we shall further describe which types of geometric hyperplanes of lie on a certain hyperbolic quadric that contains the and is invariant under its stabilizer group; in the case we shall also single out those of them that correspond, via the Lagrangian Grassmannian of type , to the set of 2295 maximal subspaces of the symplectic polar space .
Publié le :
DOI : 10.4171/aihpd/20
Mots-clés : Binary Segre varietes, Veldkamp spaces, hyperbolic quadrics
@article{AIHPD_2015__2_3_309_0, author = {Saniga, Metod and Havlicek, Hans and Holweck, Fr\'ed\'eric and Planat, Michel and Pracna, Petr}, title = {Veldkamp-space aspects of a sequence of nested binary {Segre} varieties}, journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D}, pages = {309--333}, volume = {2}, number = {3}, year = {2015}, doi = {10.4171/aihpd/20}, mrnumber = {3416838}, zbl = {1326.51004}, language = {en}, url = {http://archive.numdam.org/articles/10.4171/aihpd/20/} }
TY - JOUR AU - Saniga, Metod AU - Havlicek, Hans AU - Holweck, Frédéric AU - Planat, Michel AU - Pracna, Petr TI - Veldkamp-space aspects of a sequence of nested binary Segre varieties JO - Annales de l’Institut Henri Poincaré D PY - 2015 SP - 309 EP - 333 VL - 2 IS - 3 UR - http://archive.numdam.org/articles/10.4171/aihpd/20/ DO - 10.4171/aihpd/20 LA - en ID - AIHPD_2015__2_3_309_0 ER -
%0 Journal Article %A Saniga, Metod %A Havlicek, Hans %A Holweck, Frédéric %A Planat, Michel %A Pracna, Petr %T Veldkamp-space aspects of a sequence of nested binary Segre varieties %J Annales de l’Institut Henri Poincaré D %D 2015 %P 309-333 %V 2 %N 3 %U http://archive.numdam.org/articles/10.4171/aihpd/20/ %R 10.4171/aihpd/20 %G en %F AIHPD_2015__2_3_309_0
Saniga, Metod; Havlicek, Hans; Holweck, Frédéric; Planat, Michel; Pracna, Petr. Veldkamp-space aspects of a sequence of nested binary Segre varieties. Annales de l’Institut Henri Poincaré D, Tome 2 (2015) no. 3, pp. 309-333. doi : 10.4171/aihpd/20. http://archive.numdam.org/articles/10.4171/aihpd/20/
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