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A Remark on Non-Uniform Hyperplanes of Finite Thick Dual Polar Spaces

✍ Scribed by Harm Pralle

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 138 KB
Volume: 22
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.2001.0521

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✦ Synopsis

Let be a finite thick dual polar space, and let H be a hyperplane of . Calling the elements of of type 2 quads, we call a quad α ⊂ H singular (respectively subquadrangular or ovoidal) if H meets α in the perp of a point (respectively in a full subquadrangle or in an ovoid). A hyperplane is said to be uniform if all quads not contained in it are either singular or subquadrangular or ovoidal.

We prove that each non-uniform hyperplane H of a finite thick dual polar space meets some quad in the perp of a point.

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Uniform Hyperplanes of Finite Dual Polar

Uniform Hyperplanes of Finite Dual Polar Spaces of Rank 3

✍ A. Pasini; S. Shpectorov 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 124 KB

Let 2 be a finite thick dual polar space of rank 3. We say that a hyperplane H of 2 is locally singular (respectively, quadrangular or ovoidal) if H & Q is the perp of a point (resp. a subquadrangle or an ovoid) of Q for every quad Q of 2. If H is locally singular, quadrangular, or ovoidal, then we