Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 17 (2021), 067, 14 pages      arXiv:2009.09854      https://doi.org/10.3842/SIGMA.2021.067

A New Class of Integrable Maps of the Plane: Manin Transformations with Involution Curves

Peter H. van der Kamp
Department of Mathematics and Statistics, La Trobe University, Victoria 3086, Australia

Received January 15, 2021, in final form July 02, 2021; Published online July 13, 2021

Abstract
For cubic pencils we define the notion of an involution curve. This is a curve which intersects each curve of the pencil in exactly one non-base point of the pencil. Involution curves can be used to construct integrable maps of the plane which leave invariant a cubic pencil.

Key words: integrable map of the plane; Manin transformation; Bertini involution; invariant; pencil of cubic curves.

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