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$ \operatorname{SL}(2)$-orbit theorem for degeneration of mixed Hodge structure

Author(s): Kazuya Kato; Chikara Nakayama; Sampei Usui
Journal: J. Algebraic Geom. 17 (2008), 401-479.
Posted: October 30, 2007
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Abstract | References | Additional information

Abstract: Cattani, Kaplan and Schmid (1986) established the $ \operatorname{SL}(2)$-orbit theorem in several variables for the degeneration of polarized Hodge structure. The aim of the present paper is to generalize it for the degeneration of mixed Hodge structure whose graded quotients by the weight filtration are polarized. As an application, we obtain a mixed Hodge version of an estimate of the Hodge metric for the degeneration of polarized Hodge structure.

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Additional Information:

Kazuya Kato
Affiliation: Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto, 606-8502, Japan
Email: kzkt@math.kyoto-u.ac.jp

Chikara Nakayama
Affiliation: Department of Mathematics, Tokyo Institute of Technology, Meguro, Tokyo, 152-8551, Japan
Email: cnakayam@math.titech.ac.jp

Sampei Usui
Affiliation: Graduate School of Science, Osaka University, Toyonaka, Osaka, 560-0043, Japan
Email: usui@math.sci.osaka-u.ac.jp

PII: S 1056-3911(07)00486-9
Received by editor(s): March 18, 2006
Received by editor(s) in revised form: April 12, 2007
Posted: October 30, 2007
Additional Notes: Partly supported by the Grants-in-Aid for Scientific Research (B) 16340005, and (B) 15340009, the Ministry of Education, Culture, Sports, Science and Technology, Japan

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