Ciliberto-Miranda degenerations of $\mathbb{CP}^2$ blown up in 10 points

We simplify Ciliberto's and Miranda's method(arXiv:0812.0032) to construct degenerations of $\mathbb{CP}^2$ blown up in several points yielding lower bounds of the corresponding multi-point Seshadri constants. In particular we exploit an asymptotic result of the author (arXiv:math/0508561) which allows to check the non-specialty of much fewer linear systems on $\mathbb{CP}^2$. We obtain the lower bound 117/370 for the 10-point Seshadri constant on $\mathbb{CP}^2$.