Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

The cohomology of a variation of polarized Hodge structures over a quasi-compact Kähler manifold


Authors: Jürgen Jost, Yi-Hu Yang and Kang Zuo
Journal: J. Algebraic Geom. 16 (2007), 401-434
DOI: https://doi.org/10.1090/S1056-3911-07-00468-7
Published electronically: April 5, 2007
MathSciNet review: 2306274
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Abstract | References | Additional Information

Abstract: In this article, we consider the cohomologies with coefficients in a variation of polarized Hodge structures on a quasi-compact Kaehler manifold. We show that the $ L^2$-Dolbeault cohomology can be identified with the $ L^2$ cohomology; we also give several direct applications of the result above.


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Additional Information

Jürgen Jost
Affiliation: Max-Planck Institute for Mathematics in the Sciences, Inselstr. 22, D-04103 Leipzig, Germany
Email: jjost@mis.mpg.de

Yi-Hu Yang
Affiliation: Department of Mathematics, Tongji University, Shanghai 200092, China
Email: yhyang@mail.tongji.edu.cn

Kang Zuo
Affiliation: Department of Mathematics, University of Mainz, 55128 Mainz, Germany
Email: zuok@uni-mainz.de

DOI: https://doi.org/10.1090/S1056-3911-07-00468-7
Received by editor(s): March 1, 2005
Received by editor(s) in revised form: December 6, 2006
Published electronically: April 5, 2007
Additional Notes: The second author was partially supported by the NSF of China (No.10471105), “Shuguang Project” of the Committee of Education of Shanghai (04SG21). The third author was partially supported by the “DFG-Schwerpunktprogramm Globale Methoden in Komplexen Geometrie”.

American Mathematical Society