Year 2020, Volume 8 , Issue 2, Pages 60 - 64 2020-10-15

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

Ziya AKÇA [1] , Abdilkadir ALTINTAŞ [2]


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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Projective spaces, Fano plane, Arcs
  • [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).
Primary Language en
Subjects Mathematics
Journal Section Articles
Authors

Orcid: 0000-0001-6379-0546
Author: Ziya AKÇA (Primary Author)
Institution: ESKISEHIR OSMANGAZI UNIVERSITY, FACULTY OF SCIENCE AND LETTERS
Country: Turkey


Orcid: 0000-0002-7012-352X
Author: Abdilkadir ALTINTAŞ

Supporting Institution The Scientific Research Projects Commission of Eskisehir Osmangazi University
Project Number Project Number 2019-2542
Dates

Publication Date : October 15, 2020

Bibtex @research article { mathenot640523, journal = {Mathematical Sciences and Applications E-Notes}, issn = {}, eissn = {2147-6268}, address = {}, publisher = {Murat TOSUN}, year = {2020}, volume = {8}, pages = {60 - 64}, doi = {10.36753/mathenot.640523}, title = {A Note on Embedding the 4-arcs of Fano Plane with Quadric and Cubic Veroneseans to Projective Spaces}, key = {cite}, author = {Akça, Ziya and Altıntaş, Abdilkadir} }
APA Akça, Z , Altıntaş, 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 , 8 (2) , 60-64 . DOI: 10.36753/mathenot.640523
MLA Akça, Z , Altıntaş, A . "A Note on Embedding the 4-arcs of Fano Plane with Quadric and Cubic Veroneseans to Projective Spaces" . Mathematical Sciences and Applications E-Notes 8 (2020 ): 60-64 <https://dergipark.org.tr/en/pub/mathenot/issue/57179/640523>
Chicago Akça, Z , Altıntaş, A . "A Note on Embedding the 4-arcs of Fano Plane with Quadric and Cubic Veroneseans to Projective Spaces". Mathematical Sciences and Applications E-Notes 8 (2020 ): 60-64
RIS TY - JOUR T1 - A Note on Embedding the 4-arcs of Fano Plane with Quadric and Cubic Veroneseans to Projective Spaces AU - Ziya Akça , Abdilkadir Altıntaş Y1 - 2020 PY - 2020 N1 - doi: 10.36753/mathenot.640523 DO - 10.36753/mathenot.640523 T2 - Mathematical Sciences and Applications E-Notes JF - Journal JO - JOR SP - 60 EP - 64 VL - 8 IS - 2 SN - -2147-6268 M3 - doi: 10.36753/mathenot.640523 UR - https://doi.org/10.36753/mathenot.640523 Y2 - 2020 ER -
EndNote %0 Mathematical Sciences and Applications E-Notes A Note on Embedding the 4-arcs of Fano Plane with Quadric and Cubic Veroneseans to Projective Spaces %A Ziya Akça , Abdilkadir Altıntaş %T A Note on Embedding the 4-arcs of Fano Plane with Quadric and Cubic Veroneseans to Projective Spaces %D 2020 %J Mathematical Sciences and Applications E-Notes %P -2147-6268 %V 8 %N 2 %R doi: 10.36753/mathenot.640523 %U 10.36753/mathenot.640523
ISNAD Akça, Ziya , Altıntaş, Abdilkadir . "A Note on Embedding the 4-arcs of Fano Plane with Quadric and Cubic Veroneseans to Projective Spaces". Mathematical Sciences and Applications E-Notes 8 / 2 (October 2020): 60-64 . https://doi.org/10.36753/mathenot.640523
AMA Akça Z , Altıntaş A . A Note on Embedding the 4-arcs of Fano Plane with Quadric and Cubic Veroneseans to Projective Spaces. Math. Sci. Appl. E-Notes. 2020; 8(2): 60-64.
Vancouver Akça Z , Altıntaş A . A Note on Embedding the 4-arcs of Fano Plane with Quadric and Cubic Veroneseans to Projective Spaces. Mathematical Sciences and Applications E-Notes. 2020; 8(2): 60-64.
IEEE Z. Akça and A. Altıntaş , "A Note on Embedding the 4-arcs of Fano Plane with Quadric and Cubic Veroneseans to Projective Spaces", Mathematical Sciences and Applications E-Notes, vol. 8, no. 2, pp. 60-64, Oct. 2020, doi:10.36753/mathenot.640523