Locally singular hyperplanes in thick dual polar spaces of rank 4

Authors:
I. Cardinali;B. De Bruyn;A. Pasini
Affiliations:
Dipartimento di Scienze Matematiche e Informatiche "R. Magari", Università di Siena, Pian dei Mantellini, Siena, Italy;Department of Pure Mathematics and Computer Algebra, Ghent University, Galglaan, Gent, Belgium;Dipartimento di Scienze Matematiche e Informatiche "R. Magari", Università di Siena, Pian dei Mantellini, Siena, Italy
Venue:
Journal of Combinatorial Theory Series A
Year:
2006

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Abstract

We study (i-)locally singular hyperplanes in a thick dual polar space Δ of rank n. If Δ is not of type DQ(2n, K), then we will show that every locally singular hyperplane of Δ is singular. We will describe a new type of hyperplane in DQ(8, K) and show that every locally singular hyperplane of DQ(8, K) is either singular, the extension of a hexagonal hyperplane in a hex or of the new type.