LOCAL SPLITTING FAMILIES OF HYPERELLIPTIC PENCILS, I

Abstract

We construct local splitting families of hyperelliptic pencils so that the original complicated degenerate fiber decomposes into several simple degenerate fibers. In some sense, our trial is a generalization to hyperelliptic curves of arbitrary genus of Moishezon's construction for families of elliptic curves. Moreover, we study certain invariants of degenerate fiber germs.