Abstract
We contribute to the algebraic-geometric study of discrete integrable systems generated by planar birational maps: (a) we find geometric description of Manin involutions for elliptic pencils consisting of curves of higher degree, birationally equivalent to cubic pencils (Halphen pencils of index 1), and (b) we characterize special geometry of base points ensuring that certain compositions of Manin involutions are integrable maps of low degree (quadratic Cremona maps). In particular, we identify some integrable Kahan discretizations as compositions of Manin involutions for elliptic pencils of higher degree.
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10 June 2021
Adding the Open Access funding note to fullfill the contractual requirement of the Multiple Compact agreement.
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This research is supported by the Deutsche Forschungsgemeinschaft (DFG) Collaborative Research Center TRR 109 “Discretization in Geometry and Dynamics”.
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Petrera, M., Suris, Y.B., Wei, K. et al. Manin Involutions for Elliptic Pencils and Discrete Integrable Systems. Math Phys Anal Geom 24, 6 (2021). https://doi.org/10.1007/s11040-021-09376-4
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DOI: https://doi.org/10.1007/s11040-021-09376-4