On Quadrirational Yang-Baxter Maps - Papageorgiou, V.G.; Suris, Yu.B.; Tongas, A.G.; Veselov, A.P. (Symmetry, Integrability and Geometry: Methods and Applications, 2010)
We use the classification of the quadrirational maps given by Adler, Bobenko and Suris to describe when such maps satisfy the Yang-Baxter relation. We show that the corresponding maps can be characterized by certain singularity invariance condition. This leads to some new families of Yang-Baxter maps corresponding to the geometric symmetries of pencils of quadrics.