In this talk, I will give a list of monodromy factorizations of unity in the pure mapping class group $PMod(T^2_{d+1})$ of a torus with $d+1$ marked points, which represent lines (aka rational $(-1)$-curves) on del Pezzo surfaces $Y$ of degrees $d\leq 3$. In the case $d=1$, one can construct an explicit correspondence between the set of such factorizations and the 240 roots of $E_8=K^\perp$ (orthogonal complement in $H_2(Y)$ of the canonical class). In the cases $d=2$ and $d=3$, one can give similar correspondences with the elements $v\in K^\perp$ (lattices $E_7$ and $E_6$) with $v^2=-6$ and $v^2=-12$ respectively, representing $56$ (for $d=2$) and $27$ (for $d=3$) lines. 

This is a joint work with S. Finashin