On pencils of cubics on the projective line over finite fields of characteristic > 3

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Günay Mert, Gülizar and Lavrauw, Michel (2022) On pencils of cubics on the projective line over finite fields of characteristic > 3. Finite Fields and their Applications, 78 . ISSN 1071-5797 (Print) 1090-2465 (Online)

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Abstract

In this paper we study combinatorial invariants of the equivalence classes of pencils of cubics on PG(1,q), for q odd and q not divisible by 3. These equivalence classes are considered as orbits of lines in PG(3,q), under the action of the subgroup G≅PGL(2,q) of PGL(4,q) which preserves the twisted cubic C in PG(3,q). In particular we determine the point orbit distributions and plane orbit distributions of all G-orbits of lines which are contained in an osculating plane of C, have non-empty intersection with C, or are imaginary chords or imaginary axes of C.
Item Type: Article
Uncontrolled Keywords: Finite geometry; Symmetric tensors; Twisted cubic
Divisions: Faculty of Engineering and Natural Sciences
Depositing User: Michel Lavrauw
Date Deposited: 27 Aug 2022 15:47
Last Modified: 27 Aug 2022 15:47
URI: https://research.sabanciuniv.edu/id/eprint/43865

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