Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

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


Authors: Kazuya Kato, Chikara Nakayama and Sampei Usui
Journal: J. Algebraic Geom. 17 (2008), 401-479
DOI: https://doi.org/10.1090/S1056-3911-07-00486-9
Published electronically: October 30, 2007
MathSciNet review: 2395135
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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

DOI: https://doi.org/10.1090/S1056-3911-07-00486-9
Received by editor(s): March 18, 2006
Received by editor(s) in revised form: April 12, 2007
Published electronically: 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

American Mathematical Society