On sections of hyperelliptic Lefschetz fibrations

Abstract

We construct a relation among right-handed Dehn twists in the mapping class group of a compact oriented surface of genus $g$ with $4g+4$ boundary components. This relation gives an explicit topological description of $4g+4$ disjoint $\left(-1\right)$–sections of a hyperelliptic Lefschetz fibration of genus $g$ on the manifold ${ℂ\mathbb{P}}^2\#\left(4g+5\right){\overline{ℂ\mathbb{P}}}^2$.