Manin Involutions for Elliptic Pencils and Discrete Integrable Systems-Reference-Cited by-同舟云学术

Manin Involutions for Elliptic Pencils and Discrete Integrable Systems

Published:2021-03 Issue:1 Volume:24 Page:
ISSN:1385-0172
Container-title:Mathematical Physics, Analysis and Geometry
language:en
Short-container-title:Math Phys Anal Geom

Author:

Petrera Matteo,Suris Yuri B.^ORCID,Wei Kangning,Zander René

Abstract

AbstractWe 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.

Funder

Deutsche Forschungsgemeinschaft

Publisher

Springer Science and Business Media LLC

Subject

Geometry and Topology,Mathematical Physics

Link

https://link.springer.com/content/pdf/10.1007/s11040-021-09376-4.pdf

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