Tohoku Mathematical Journal
2001
September
SECOND SERIES VOL. 53, NO. 3

Tohoku Math. J.
53 (2001), 369-394

Title LOCAL SPLITTING FAMILIES OF HYPERELLIPTIC PENCILS

Author Tatsuya Arakawa and Tadashi Ashikaga

(Received June 22, 1999, revised January 31, 2001)
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.

2000 Mathematics Subject Classification. Primary 14H15; Secondary 14J29, 14J17, 14H45, 30F10.

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