Let P be a finite classical polar space of rank d. An m-regular system with respect to (k−1)-dimensional projective spaces of P, 1≤k≤d−1, is a set R of generators of P with the property that every (k−1)-dimensional projective space of P lies on exactly m generators of R. Regular systems of polar spaces are investigated. Some non-existence results about certain 1-regular systems of polar spaces with low rank are proved and a procedure to obtain m′-regular systems from a given m-regular system is described. Finally, three different construction methods of regular systems w.r.t. points of various polar spaces are discussed.

On regular systems of finite classical polar spaces

Pavese F.
;
2022

Abstract

Let P be a finite classical polar space of rank d. An m-regular system with respect to (k−1)-dimensional projective spaces of P, 1≤k≤d−1, is a set R of generators of P with the property that every (k−1)-dimensional projective space of P lies on exactly m generators of R. Regular systems of polar spaces are investigated. Some non-existence results about certain 1-regular systems of polar spaces with low rank are proved and a procedure to obtain m′-regular systems from a given m-regular system is described. Finally, three different construction methods of regular systems w.r.t. points of various polar spaces are discussed.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/244751
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