Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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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.

Motivicity of the mixed Hodge structure of some degenerations of curves

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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