Local splitting families of hyperelliptic pencils, I

We construct local splitting fan-Lilies of hyperelliptic pencils so that th e original complicated degenerate fiber decomposes into several simple dege nerate fibers. In some sense, our trial is a generalization to hyperellipti c curves of arbitrary genus of Moishezon's construction for families of ell iptic curves. Moreover, we study certain invariants of degenerate fiber ger ms.