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

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dc.creatorAdler, V. E.
dc.creatorBobenko, A. I.
dc.creatorSuris, Yu. B.
dc.date2003-07-01
dc.date.accessioned2026-07-07T08:06:09Z
dc.date.available2026-07-07T08:06:09Z
dc.descriptionBirational Yang-Baxter maps (`set-theoretical solutions of the Yang-Baxter equation') are considered. A birational map $(x,y)\mapsto(u,v)$ is called quadrirational, if its graph is also a graph of a birational map $(x,v)\mapsto(u,y)$. We obtain a classification of quadrirational maps on $\CP^1\times\CP^1$, 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.
dc.descriptionLaTeX, 40pp, 3 Figs
dc.identifierhttps://arxiv.org/abs/math/0307009
dc.identifierhttp://arxiv.org/abs/math/0307009
dc.identifierCommun. Anal. Geom., 2004, vol. 12, p. 967-1007
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130510
dc.subjectQuantum Algebra
dc.subjectMathematical Physics
dc.subjectAlgebraic Geometry
dc.subjectExactly Solvable and Integrable Systems
dc.titleGeometry of Yang--Baxter maps: pencils of conics and quadrirational mappings
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