Geometry of Yang – Baxter Maps : pencils of conics and quadrirational mappings

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 × CP, and show that all of them satisfy the Yang-Baxter equation. These maps… CONTINUE READING