SavedAdd your journal

Journals / Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi / 2022 / Cilt: 38 Sayı: 3

On The Projective Planes In Projective Space PG(4,4)

PG(4,4) Projektif Uzayındaki Projektif Düzlemler Üzerine

Süheyla Ekmekçi(ESKİŞEHİR OSMANGAZİ ÜNİVERSİTESİ)0000-0003-2820-2096
Ayşe Bayar(ESKİŞEHİR OSMANGAZİ ÜNİVERSİTESİ)0000-0002-2210-5423
Ziya Akça(ESKİŞEHİR OSMANGAZİ ÜNİVERSİTESİ)0000-0001-6379-0546
Pages
519–524
Publication Date
2022-12-30
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Then taking points span PG(4,4), the projective plane of order 4 isdetermined such that every line of the plane is a conic plane in PG(4,4).

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, firstly, it is shown that the geometric structure, which isthe image under the projection and the Veronesean map of the projective planeover the field GF(4) is the projective plane of order 4 such that the set of pointsspans PG(4,4) and the lines set consists of conics in PG(4,4) by introducing withcoordinates.
📊
Key Findings & Data:In this study, firstly, it is shown that the geometric structure, which isthe image under the projection and the Veronesean map of the projective planeover the field GF(4) is the projective plane of order 4 such that the set of pointsspans PG(4,4) and the lines set consists of conics in PG(4,4) by introducing withcoordinates.
💡
Conclusion & Impact:Then taking points span PG(4,4), the projective plane of order 4 isdetermined such that every line of the plane is a conic plane in PG(4,4).
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Projektif Uzay · Projektif Düzlem · Veronesean Dönüşüm

Abstract

In this study, firstly, it is shown that the geometric structure, which isthe image under the projection and the Veronesean map of the projective planeover the field GF(4) is the projective plane of order 4 such that the set of pointsspans PG(4,4) and the lines set consists of conics in PG(4,4) by introducing withcoordinates. Then taking points span PG(4,4), the projective plane of order 4 isdetermined such that every line of the plane is a conic plane in PG(4,4).

Özet

Bu çalışmada önce GF(4) cismi üzerindeki projektif düzlemin Veroneseandönüşüm ve izdüşüm altında görüntüsü olan geometrik yapının, noktalar kümesiPG(4,4) projektif uzayını geren noktalardan ve doğrular kümesi PG(4,4)uzayındaki koniklerden oluşan, 4. mertebeden projektif düzlem olduğukoordinatlarının sunumu ile verilmektedir. Daha sonra PG(4,4) uzayını gerennoktalar kümesi alınarak, doğruları konik düzlemleri olan 4. mertebeden projektifdüzlem koordinatları belirlenmektedir.

🔖

Cite This Article

Ekmekçi, S., Bayar, A., Akça, Z. (2022). On The Projective Planes In Projective Space PG(4,4). Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi, Cilt: 38 Sayı: 3, 519–524. https://ajindex.com/articles/1266777

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (9)

  1. References [1] Akça Z., Bayar A., Ekmekci S., R., Kaya, Thas J. A. and Maldeghem H. Van, 2012. Generalized Veronesean embeddings of projective spaces, Part II. The lax case. Ars Combinatoria, CIII, pp. 65-80.
  2. Cossidente,A., Labbate,D., Sicilino,A., 2001. Veronese Varieties Over Finite Fields and Their Prpjections. Design, Codes and Cryptography, 22, 19-32.
  3. Hirschfeld J.W.P., 1979. Projective Geometries over finite fields, Clarendon Press, Oxford.
  4. Hirschfeld J.W.P., Thas J.A., 2016. General Galois Geometries, Springer Monographs in Mathematics, Springer-Verlag London, 143-195.
  5. Kaya R., 2005. Projektif Geometri, Osmangazi Üniversitesi Yayınları, Eskişehir.
  6. Mazzocca, F. and Melone, N., 1984. Caps and Veronese Varieties In Projective Galois Spaces. Discrete Mathematics, 48, 243-252.
  7. Melone, N., 1983. Veronese Spaces. Journal of Geometri, 20, 169-180.
  8. Thas J.A. and Maldeghem H. Van, 2004. Classification of Finite Veronesean Caps. European Journal of Combinatorics, 25, 275-285.
  9. Thas J.A. and Maldeghem H. Van, 2011. Generalized Veronesean embeddings of projective spaces. Combinatorica, 31 (5), 615-629.