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Characterisations and classifications in the theory of parapolar spaces

(2019)
Author
Promoter
(UGent) and Jeroen Schillewaert
Organization
Abstract
This thesis in incidence geometry is divided into two parts, which can both be linked to the geometries of the Freudenthal-Tits magic square. The first and main part consists of an axiomatic characterisation of certain plane geometries, defined via the Veronese mapping using degenerate quadratic alternative algebras (over any field) with a radical that is (as a ring) generated by a single element. This extends and complements earlier results of Schillewaert and Van Maldeghem, who considered such geometries over non-degenerate quadratic alternative algebras. The second and smaller part deals with a classification of parapolar spaces exhibiting the feature that the dimensions of intersections of pairs of symplecta cannot take all possible sensible values, with the only further requirement that, if the parapolar spaces have symplecta of rank 2, then they are strong. This part is based on a joint work with Schillewaert, Van Maldeghem and Victoor.
Keywords
Parapolar spaces, Veronese varieties

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Citation

Please use this url to cite or link to this publication:

Chicago
De Schepper, Anneleen. 2019. “Characterisations and Classifications in the Theory of Parapolar Spaces”. Ghent, Belgium: Ghent University. Faculty of Sciences.
APA
De Schepper, Anneleen. (2019). Characterisations and classifications in the theory of parapolar spaces. Ghent University. Faculty of Sciences, Ghent, Belgium.
Vancouver
1.
De Schepper A. Characterisations and classifications in the theory of parapolar spaces. [Ghent, Belgium]: Ghent University. Faculty of Sciences; 2019.
MLA
De Schepper, Anneleen. “Characterisations and Classifications in the Theory of Parapolar Spaces.” 2019 : n. pag. Print.
@phdthesis{8616828,
  abstract     = {This thesis in incidence geometry is divided into two parts, which can both be linked to the geometries of the Freudenthal-Tits magic square. 
The first and main part consists of an axiomatic characterisation of certain plane geometries, defined via the Veronese mapping using degenerate quadratic alternative algebras (over any field) with a radical that is (as a ring) generated by a single element. This extends and complements earlier results of Schillewaert and Van Maldeghem, who considered such geometries over non-degenerate quadratic alternative algebras.
The second and smaller part deals with a classification of parapolar spaces exhibiting the feature that the dimensions of intersections of pairs of symplecta cannot take all possible sensible values, with the only further requirement that, if the parapolar spaces have symplecta of rank 2, then they are strong. This part is based on a joint work with Schillewaert, Van Maldeghem and Victoor.},
  author       = {De Schepper, Anneleen},
  language     = {eng},
  pages        = {IX, 233},
  publisher    = {Ghent University. Faculty of Sciences},
  school       = {Ghent University},
  title        = {Characterisations and classifications in the theory of parapolar spaces},
  year         = {2019},
}