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Desargues Theorem, Dynamics, and Hyperplane Arrangements

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Abstract

The Desargues theorem is a basic theorem in classical projective geometry. In this paper we generalize Desargues theorem in the direction of dynamical systems. Our result comprises an infinite family of configurations, having unbounded complexity. The proof of the result involves constructing special kinds of hyperplane arrangements and then projecting subsets of them into the plane.

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References

  • [K] Kendig, K.: Elementary Algebraic Geometry, Graduate Text in Math. 44, Springer-Verlag, Berlin, 1977.

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  • [S] Schwartz, R.: The pentagram map, J. Experimental Math. 1992.

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Authors and Affiliations

  1. Department of Mathematics, Room 4116, University of Maryland, College Park, MD, 20742-4015, U.S.A.

    Richard Evan Schwartz

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  1. Richard Evan Schwartz
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Schwartz, R.E. Desargues Theorem, Dynamics, and Hyperplane Arrangements. Geometriae Dedicata 87, 261–283 (2001). https://doi.org/10.1023/A:1012016602813

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  • DOI: https://doi.org/10.1023/A:1012016602813

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