Harmonic maps and singularities of period mappings
HTML articles powered by AMS MathViewer
- by Jürgen Jost, Yi-Hu Yang and Kang Zuo PDF
- Proc. Amer. Math. Soc. 143 (2015), 3351-3356 Request permission
Abstract:
We use simple methods from harmonic maps to investigate singularities of period mappings at infinity. More precisely, we derive a harmonic map version of Schmid’s nilpotent orbit theorem.References
- Eduardo Cattani, Aroldo Kaplan, and Wilfried Schmid, Degeneration of Hodge structures, Ann. of Math. (2) 123 (1986), no. 3, 457–535. MR 840721, DOI 10.2307/1971333
- Maurizio Cornalba and Phillip Griffiths, Analytic cycles and vector bundles on non-compact algebraic varieties, Invent. Math. 28 (1975), 1–106. MR 367263, DOI 10.1007/BF01389905
- Phillip Griffiths (ed.), Topics in transcendental algebraic geometry, Annals of Mathematics Studies, vol. 106, Princeton University Press, Princeton, NJ, 1984. MR 756842, DOI 10.1515/9781400881659
- Phillip Griffiths and Wilfried Schmid, Locally homogeneous complex manifolds, Acta Math. 123 (1969), 253–302. MR 259958, DOI 10.1007/BF02392390
- Jürgen Jost, Riemannian geometry and geometric analysis, 6th ed., Universitext, Springer, Heidelberg, 2011. MR 2829653, DOI 10.1007/978-3-642-21298-7
- Jürgen Jost, Partial differential equations, 3rd ed., Graduate Texts in Mathematics, vol. 214, Springer, New York, 2013. MR 3012036, DOI 10.1007/978-1-4614-4809-9
- Jürgen Jost, Yi-Hu Yang, and Kang Zuo, Cohomologies of unipotent harmonic bundles over noncompact curves, J. Reine Angew. Math. 609 (2007), 137–159. MR 2350782, DOI 10.1515/CRELLE.2007.062
- J. Jost, Y.-H. Yang, and K. Zuo, Harmonic metrics on unipotent bundles over quasi-compact Kähler manifolds. Preprint.
- Bertram Kostant, The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group, Amer. J. Math. 81 (1959), 973–1032. MR 114875, DOI 10.2307/2372999
- Zhiqin Lu, On the geometry of classifying spaces and horizontal slices, Amer. J. Math. 121 (1999), no. 1, 177–198. MR 1705002
- Zhiqin Lu and Xiaofeng Sun, Weil-Petersson geometry on moduli space of polarized Calabi-Yau manifolds, J. Inst. Math. Jussieu 3 (2004), no. 2, 185–229. MR 2055709, DOI 10.1017/S1474748004000076
- Wilfried Schmid, Variation of Hodge structure: the singularities of the period mapping, Invent. Math. 22 (1973), 211–319. MR 382272, DOI 10.1007/BF01389674
- Carlos T. Simpson, Harmonic bundles on noncompact curves, J. Amer. Math. Soc. 3 (1990), no. 3, 713–770. MR 1040197, DOI 10.1090/S0894-0347-1990-1040197-8
- Steven Zucker, Hodge theory with degenerating coefficients. $L_{2}$ cohomology in the Poincaré metric, Ann. of Math. (2) 109 (1979), no. 3, 415–476. MR 534758, DOI 10.2307/1971221
Additional Information
- Jürgen Jost
- Affiliation: Max-Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany
- Email: jjost@mis.mpg.de
- Yi-Hu Yang
- Affiliation: Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, People’s Republic of China
- Email: yangyihu@sjtu.edu.cn
- Kang Zuo
- Affiliation: Department of Mathematics, Mainz University, 55099 Mainz, Germany
- MR Author ID: 269893
- Email: zuok@uni-mainz.de
- Received by editor(s): December 18, 2013
- Published electronically: April 16, 2015
- Additional Notes: The first author was partially supported by ERC Advanced Grant FP7-267087
The second author was partially supported by NSF of China (No. 11171253) - Communicated by: Lei Ni
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 3351-3356
- MSC (2010): Primary 14M27, 58E20
- DOI: https://doi.org/10.1090/proc/12566
- MathSciNet review: 3348777