Geometry of Yang-Baxter maps: Pencils of conics and quadrirational mappings

V. E. Adler, A. I. Bobenko, Yu B. Suris

Publikation: Beitrag in FachzeitschriftArtikelBegutachtung

63 Zitate (Scopus)

Abstract

Birational Yang-Baxter maps ('set-theoretical solutions of the Yang-Baxter equation') are considered. A birational map (x,y) → (u,v) is called quadrirational, if its graph is also a graph of a birational map (x,v) → (u,y). We obtain a classification of quadrirational maps on ℂℙ 1 × ℂℙ1, and show that all of them satisfy the Yang-Baxter equation. These maps possess a nice geometric interpretation in terms of linear pencil of conics, the Yang-Baxter property being interpreted as a new incidence theorem of the projective geometry of conics.

OriginalspracheEnglisch
Seiten (von - bis)967-1007
Seitenumfang41
FachzeitschriftCommunications in Analysis and Geometry
Jahrgang12
Ausgabenummer5
DOIs
PublikationsstatusVeröffentlicht - Dez. 2004
Extern publiziertJa

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