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Journals / Turkish Journal of Mathematics / 2019 / Cilt: 43 - Sayı: 4

Cremona transformations of plane configurations of 6 points

Remziye Arzu ZABUN
Pages
1837–1849
Publication Date
2022-11-04
DOI
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AI Summary & Key Takeaways

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

As an application, we give an alternative approach to determining thedeformation types (i.e. icosahedral, bipartite, tripartite and hexagonal) of 36 real Schläfli double sixes on any nonsingularreal cubic surface performed by Segre.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We analyze how a set of 6 points of $RP^2$ in general position changes under quadratic Cremona transformationsbased at triples of points of the given six.
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Key Findings & Data:We analyze how a set of 6 points of $RP^2$ in general position changes under quadratic Cremona transformationsbased at triples of points of the given six.
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Conclusion & Impact:As an application, we give an alternative approach to determining thedeformation types (i.e. icosahedral, bipartite, tripartite and hexagonal) of 36 real Schläfli double sixes on any nonsingularreal cubic surface performed by Segre.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

We analyze how a set of 6 points of $RP^2$ in general position changes under quadratic Cremona transformationsbased at triples of points of the given six. As an application, we give an alternative approach to determining thedeformation types (i.e. icosahedral, bipartite, tripartite and hexagonal) of 36 real Schläfli double sixes on any nonsingularreal cubic surface performed by Segre.

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Cite This Article

ZABUN, R. A. (2022). Cremona transformations of plane configurations of 6 points. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 4, 1837–1849. https://ajindex.com/articles/608062

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References (7)

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  2. Cremona L. Sulle transformazioni geometriche delle figure piane. Mem Accad Bologna (2) 5, 1865; 62: 3-35 (in Italian)
  3. Finashin S. Projective configurations and real algebraic curves. PhD, Leningrad State University, Saint Petersburg, Russia, 1985
  4. Finashin S, Zabun RA. Deformation classification of typical configurations of 7 points in the real projective plane. Topology and its Applications, 2015; 194: pp. 358-385
  5. Finashin S, Zabun RA. Topology of real Schlafli six-line configurations on cubic surfaces and in RP3. Proceedings of the American Mathematical Society, 2018; doi:
  6. Schläfli L. An attempt to determine the twenty-seven lines upon a surface of the third order, and to divide such surfaces into species in reference to the reality of the lines upon the surface. Quarterly Journal of Pure and Applied Mathematics 2, 1858; pp. 55-65
  7. Segre B. The Non-Singular Cubic Surfaces. A New Method of Investigation with Special Reference to Questions of Reality. London, England: Oxford, The Clarendon Press, 1942.