Veldkamp-space aspects of a sequence of nested binary Segre varieties

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61388955%3A_____%2F15%3A00454032" target="_blank" >RIV/61388955:_____/15:00454032 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.4171/AIHPD/20" target="_blank" >http://dx.doi.org/10.4171/AIHPD/20</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4171/AIHPD/20" target="_blank" >10.4171/AIHPD/20</a>

Result language

angličtina

Original language name

Veldkamp-space aspects of a sequence of nested binary Segre varieties

Original language description

Let S(N)=PG(1,2)xPG(1,2)x...xPG(1,2) be a Segre variety that is an NN-fold direct product of projective lines of size three. Given two geometric hyperplanes H´H´ and H´´H´´ of S(N), let us call the triple {H´,H´´,H´ΔH´´} the Veldkamp line of S(N). We shall demonstrate, for the sequence 2<=N<=42<=N<=4, that the properties of geometric hyperplanes of S(N) are fully encoded in the properties of Veldkamp of S(N−1). Using this property, a complete classification of all types of geometric hyperplanes of S(4) is provided. Employing the fact that, for 2<=N<=42<=N<=4, the (ordinary part of) Veldkamp space of S(N) is PG(2N−1,2), we shall further describe which types of geometric hyperplanes of S(N) lie on a certain hyperbolic quadric Q+0(2N−1,2)cPG(2N−1,2) that contains the S(N) and is invariant under its stabilizer group in the N=4 case we shall also single out those of them that correspond, via the Lagrangian Grassmannian of type LG(4,8), to the set of 2295 maximal subspaces of the symplectic polar space W(7,2).

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10403 - Physical chemistry

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2015

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Annales de l’Institut Henri Poincaré D

ISSN

2308-5827

e-ISSN

—

Volume of the periodical

2

Issue of the periodical within the volume

3

Country of publishing house

CH - SWITZERLAND

Number of pages

25

Pages from-to

309-333

UT code for WoS article

000441468400003

EID of the result in the Scopus database

2-s2.0-85017438113