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

Year 2020, Volume: 8 Issue: 2, 60 - 64, 15.10.2020

Ziya Akça , Abdilkadir Altıntaş

https://doi.org/10.36753/mathenot.640523

Abstract

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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Keywords

Projective spaces, Fano plane, Arcs

Supporting Institution

The Scientific Research Projects Commission of Eskisehir Osmangazi University

Project Number

Project Number 2019-2542

References

• [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.
• [4] Ekmekçi, S., Bayar, A., Akça, Z.: P G(4, 4) Projektif Uzayındaki Projektif Düzlemler Üzerine, Ogü Bap Proje No: 201619D37, 2017.
• [5] Hirschfeld, H., Thas.,J. A.: 2016, General Galois Geometries, Springer Monongraphs in Mathematics.
• [6] Thas, J.A., Van Maldeghem, H.: Characterizations of quadric and Hermitian Veroneseans over finite fields, J. of Geometry, 76, 282-293 (2003).
• [7] Thas, J. A., Van Maldeghem, H.: Classification of finite Veronesean caps, European J. of Combin. 25, 275-285 (2004).
• [8] Thas, J. A., Van Maldeghem, H.: Characterizations of the finite quadric Veroneseans , Quart. J. Math, 55, 99-113 (2004).