Bull. Korean Math. Soc. 2010; 47(3): 593-610
Printed May 1, 2010
https://doi.org/10.4134/BKMS.2010.47.3.593
Copyright © The Korean Mathematical Society.
Hi-joon Chae and Byungheup Jun
Hongik University and Konkuk University
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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