On the stable reduction of pencils of curves (Q1113959)

Let f:S\(\to C\) be a one-dimensional family of complex projective curves of genus \(g\geq 2\). There is a base extension of degree \(N_ g\) such that the pull-back family has semi-stable reduction, where \[ N_ g=\prod_{p=prime,p\leq 2g+1}p^{\ell_ p}, \] where \(\ell_ p\) is the largest integer such that \(2g\geq p^{\ell_ p}-p^{\ell_ p-1}\).