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We consider a degeneration of genus 2 curves, which is op- posite to maximal degeneration in a sense. Such a degeneration of curves yields a variation of mixed Hodge structure with monodromy weight fil- tration. The mixed Hodge structure at each fibre, which is dierent from the limit mixed Hodge structure of Schmid and Steenbrink, can be real- ized as H1 of a noncompact singular elliptic curve. We also prove that the pull back of the above variation of mixed Hodge structure to a dou- ble cover of the base space comes from a family of noncompact singular elliptic curves.

MOTIVICITY OF THE MIXED HODGE STRUCTURE OF SOME DEGENERATIONS OF CURVES