Local deformation of pencil of curves of genus two (Q1117998)

Here are studied (locally around a singular fiber) the local deformations of a genus-2 fibration \(g:\quad S\to D,\) D one-dimensional disc; essentially it is proved how certain singular fibers can be splitted by a deformation into a union of a certain number of singular fibers of a given (easier) type. The result is related to the construction of a family of deformations (with simultaneous resolution) of elliptic double points.