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Some incidence theorems and integrable discrete equations

V. E. Adler
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Abstract

Several incidence theorems of planar projective geometry are considered. It is demonstrated that generalizations of Pascal theorem due to Möbius give rise to double cross-ratio equation and Hietarinta equation. The construction corresponding to the double cross-ratio equation is a reduction to a conic section of some planar configuration $(20_3 15_4)$. This configuration provides a correct definition of the multidimensional quadrilateral lattices on the plane.

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V. E. Adler. 2004-09-30. Some incidence theorems and integrable discrete equations. https://doi.org/10.1007/s00454-006-1254-3

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