Manin Involutions for Elliptic Pencils and Discrete Integrable Systems

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

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

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.

Original languageEnglish
Article number6
JournalMathematical Physics Analysis and Geometry
Volume24
Issue number1
DOIs
StatePublished - Mar 2021
Externally publishedYes

Keywords

  • Birational map
  • Elliptic curve
  • Elliptic pencil
  • Integrable map

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