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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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).

Název v anglickém jazyce

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

Popis výsledku anglicky

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).

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10403 - Physical chemistry

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

Annales de l’Institut Henri Poincaré D

ISSN

2308-5827

e-ISSN

—

Svazek periodika

2

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

25

Strana od-do

309-333

Kód UT WoS článku

000441468400003

EID výsledku v databázi Scopus

2-s2.0-85017438113