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 Motivicity of the mixed Hodge structure of some degenerations of curves Bull. Korean Math. Soc. 2010 Vol. 47, No. 3, 593-610 https://doi.org/10.4134/BKMS.2010.47.3.593Published online May 1, 2010 Hi-joon Chae and Byungheup Jun Hongik University and Konkuk University Abstract : We consider a degeneration of genus 2 curves, which is opposite to maximal degeneration in a sense. Such a degeneration of curves yields a variation of mixed Hodge structure with monodromy weight filtration. The mixed Hodge structure at each fibre, which is different from the limit mixed Hodge structure of Schmid and Steenbrink, can be realized as $H^1$ of a noncompact singular elliptic curve. We also prove that the pull back of the above variation of mixed Hodge structure to a double cover of the base space comes from a family of noncompact singular elliptic curves. Keywords : variation of mixed Hodge structure MSC numbers : 32G20, 32S40 Downloads: Full-text PDF