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Dergiler / Mathematical Sciences and Applications E-Notes / 2020 / Cilt: 8 - Sayı: 2

A Note on Embedding the 4− arcs of Fano Plane with Quadric and Cubic Veroneseans to Projective Spaces

Ziya AKÇA
Abdilkadir ALTINTAŞ
Sayfa
60–64
DOI
—
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In this work, we present SCID properties spaces generated by 4-arcs of Fano plane.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:The 3−spaces generate intersect pairwise in at least a line (each pair of 4−sets share two points).
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Temel Bulgular & Veri:But since the union of two such 4-sets is a 6-set, this union generates the whole space, so they pairwise intersect in a line.
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Sonuç & Katkı:In this work, we present SCID properties spaces generated by 4-arcs of Fano plane.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Özet

The 3−spaces generate intersect pairwise in at least a line (each pair of 4−sets share two points). But since the union of two such 4-sets is a 6-set, this union generates the whole space, so they pairwise intersect in a line. Dually, the lines that we consider have empty intersection. Other examples of such sets are spreads of lines, or spreads of any kind. In this work, we present SCID properties spaces generated by 4-arcs of Fano plane.

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Bu Makaleye Atıf Yap

AKÇA, Z., ALTINTAŞ, A. (2020). A Note on Embedding the 4− arcs of Fano Plane with Quadric and Cubic Veroneseans to Projective Spaces. Mathematical Sciences and Applications E-Notes, Cilt: 8 - Sayı: 2, 60–64. https://ajindex.com/articles/341472

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Kaynakça (7)

  1. Akça, Z., Bayar, A., Ekmekçi, S., Kaya, R., Thas, J. A., Van Maldeghem, H.: Generalized Veronesean embeddings of projective spaces, Part II. The lax case, Ars Combinatoria, Volume CIII, January, 2012, 65-80
  2. Akça, Z., Bayar, A., Ekmekçi, S., Kaya, R., Van Maldeghem, H.: Bazı Geometrilerin Sonlu Projektif Uzaylara Gömülmeleri Üzerine, Tübitak Proje No: 108T340, 2010 [3] Bayar, A., Akça, Z., Ekmekçi, S.: 4.Mertebeden Projektif Düzlemin 4-boyutlu Projektif Uzaya Gömülmesi Üzerine, Ogü Bap Proje No: 201619D38, 2017
  3. Ekmekçi, S., Bayar, A., Akça, Z.: P G(4, 4) Projektif Uzayındaki Projektif Düzlemler Üzerine, Ogü Bap Proje No: 201619D37, 2017
  4. Hirschfeld, H., Thas.,J. A.: 2016, General Galois Geometries, Springer Monongraphs in Mathematics
  5. Thas, J.A., Van Maldeghem, H.: Characterizations of quadric and Hermitian Veroneseans over finite fields, J. of Geometry, 76, 282-293 (2003)
  6. Thas, J. A., Van Maldeghem, H.: Classification of finite Veronesean caps, European J. of Combin. 25, 275-285 (2004)
  7. Thas, J. A., Van Maldeghem, H.: Characterizations of the finite quadric Veroneseans, Quart. J. Math, 55, 99-113 (2004)