We employ a certain labeled finite graph, called a chart, in a closed oriented surface
to describe the monodromy of a(n achiral) Lefschetz fibration over the surface.
Applying charts and their moves with respect to Wajnryb’s presentation of mapping
class groups, we first generalize a signature formula for Lefschetz fibrations over the
–sphere
obtained by Endo and Nagami to that for Lefschetz fibrations over arbitrary closed
oriented surface. We then prove two theorems on stabilization of Lefschetz fibrations
under fiber summing with copies of a typical Lefschetz fibration as generalizations of
a theorem of Auroux.