Geometry of two- and three-dimensional integrable systems related to affine Weyl groups $W(E_8^{(1)})$ and $W(E_7^{(1)})$

Jaume Alonso, Yuri B. Suris

We find a general framework for the construction of birational involutions on two- and three-dimensional varieties obtained from ${\mathbb{P}}^2$, ${\mathbb{P}}^1\times {\mathbb{P}}^1$, and…