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.2010.47.3.593
Published 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
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