✦ LIBER ✦

A characterization of projective 3-spaces

✍ Scribed by N. Durante; K. Metsch

Publisher: John Wiley and Sons
Year: 1996
Tongue: English
Weight: 621 KB
Volume: 4
Category: Article
ISSN: 1063-8539
DOI: 10.1002/(sici)1520-6610(1996)4:5<377::aid-jcd6>3.0.co;2-c

No coin nor oath required. For personal study only.

✦ Synopsis

It is known that if L is a nondegenerate linear space with II points and if P is a point of L, there exist at least 1 . -fi] lines that do not contain P with equality iff L is a projective plane. This result is stronger than the famous de Bruijn-Erdos Theorem, which states that every nondegenerate linear space has at least as many lines as points with equality iff it is a projective plane. We prove the following analogous theorem for planar spaces. Suppose that s is a planar space with p3 + p2 + p + 1 points for a real number p > 1. If P is a point of s, then there exist at least p3 planes that do not contain P with equality if and only if p is a prime power and s is the projective 3-space PG(3, p).

📜 SIMILAR VOLUMES

A Characterization of Grassmann Spaces o

A Characterization of Grassmann Spaces of Index h of a Projective Space

✍ Eva Ferrara Dentice 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 186 KB

Classification of Embeddings of the Flag

Classification of Embeddings of the Flag Geometries of Projective Planes in Finite Projective Spaces, Part 3

✍ Joseph A. Thas; Hendrik Van Maldeghem 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 214 KB

The flag geometry 1=(P, L, I) of a finite projective plane 6 of order s is the generalized hexagon of order (s, 1) obtained from 6 by putting P equal to the set of all flags of 6, by putting L equal to the set of all points and lines of 6, and where I is the natural incidence relation (inverse conta

Characterizing projective spaces on defo

Characterizing projective spaces on deformations of Hilbert schemes of K3 surfaces

✍ David Harvey; Brendan Hassett; Yuri Tschinkel 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 182 KB

On Caps and Cap Partitions of Galois Pro

On Caps and Cap Partitions of Galois Projective Spaces

✍ Cossidente, A.; King, O.H. 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 176 KB

Classification of Embeddings of the Flag

Classification of Embeddings of the Flag Geometries of Projective Planes in Finite Projective Spaces, Part 1

✍ Joseph A. Thas; Hendrik Van Maldeghem 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 156 KB

Classification of Embeddings of the Flag

Classification of Embeddings of the Flag Geometries of Projective Planes in Finite Projective Spaces, Part 2

✍ Joseph A. Thas; Hendrik Van Maldeghem 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 173 KB