Manin involutions for elliptic pencils and discrete integrable systems
Exactly Solvable and Integrable Systems
2023-04-05 v1 Mathematical Physics
Algebraic Geometry
math.MP
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.
Keywords
Cite
@article{arxiv.2008.08308,
title = {Manin involutions for elliptic pencils and discrete integrable systems},
author = {Matteo Petrera and Yuri B. Suris and Kangning Wei and Rene Zander},
journal= {arXiv preprint arXiv:2008.08308},
year = {2023}
}
Comments
22 pp, 3 figures