Hostname: page-component-848d4c4894-ndmmz Total loading time: 0 Render date: 2024-05-18T15:26:32.779Z Has data issue: false hasContentIssue false
  • English
  • Français

On the boundary of moduli spaces of log Hodge structures, II: Nontrivial torsors

Published online by Cambridge University Press:  11 January 2016

Tatsuki Hayama
Tatsuki Hayama*
Affiliation:
Department of Mathematics National Taiwan University, Taipei 106, Taiwan
*
Mathematical Sciences Center, Tsinghua University, Haidian District, Beijing 100084, China, tatsuki@math.tsinghua.edu.cn
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we determine when a natural torsor arising in the work of Kato and Usui on partial compactification of period domains of pure Hodge structure is trivial, and we give an application to cycle spaces.

Keywords

32G20
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 213 , March 2014 , pp. 1 - 20
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2014

References

[AMRT] Ash, A., Mumford, D., Rapoport, M., and Tai, Y.-S., Smooth Compactification of Locally Symmetric Varieties, Math. Sci. Press, Brookline, Massachusetts, 1975. MR 0457437.Google Scholar
[CMP] Carlson, J., Müller-Stach, S., and Peters, C., Period Mappings and Period Domains, Cambridge Stud. Adv. Math. 85, Cambridge University Press, Cambridge, 2003. MR 2012297.Google Scholar
[CKS] Cattani, E., Kaplan, A., and Schmid, W., Degeneration of Hodge structures, Ann. of Math. (2) 123 (1986), 457–535. MR 0840721. DOI 10.2307/1971333.Google Scholar
[FHW] Fels, G., Huckleberry, A., and Wolf, J. A., Cycle Spaces of Flag Domains: A Complex Geometric Viewpoint, Progr. Math. 245, Birkhäuser, Boston, 2006. MR 2188135.Google Scholar
[F] Fulton, W., Introduction to Toric Varieties, Ann. of Math. Stud. 131, Princeton University Press, Princeton, 1993. MR 1234037.Google Scholar
[GGK1] Green, M., Griffiths, P., and Kerr, M., “Néron models and boundary components for degenerations of Hodge structures of mirror quintic type” in Curves and Abelian Varieties, Contemp. Math. 465, Amer. Math. Soc., 2008, 71–145. MR 2457736. DOI 10.1090/conm/465/09101.CrossRefGoogle Scholar
[GGK2] Green, M., Mumford-Tate Groups and Domains: Their Geometry and Arithmetic, Ann. of Math. Stud. 183, Princeton University Press, Princeton, 2012. MR 2918237.Google Scholar
[G] Griffiths, P., Periods of integrals on algebraic manifolds, I: Construction and properties of the modular varieties, Amer. J. Math. 90 (1968), 568–626. MR 0229641.Google Scholar
[H1] Hayama, T., On the boundary of the moduli spaces of log Hodge structures: Triviality of the torsor, Nagoya Math. J. 198 (2010), 173–190. MR 2666580.Google Scholar
[H2] Hayama, T., Boundaries of cycle spaces and degenerating Hodge structures, to appear in Asian J. Math, preprint, arXiv:1203.6770v3 [math.AG].Google Scholar
[KU] Kato, K. and Usui, S., Classifying Spaces of Degenerating Polarized Hodge Structures, Ann. of Math. Stud. 169, Princeton University Press, Princeton, 2009. MR 2465224.Google Scholar
[KP] Kerr, M. and Pearlstein, G., Boundary components of Mumford-Tate domains, preprint, arXiv:1210.5301v1 [math.AG].Google Scholar
[LS] Lu, Z. and Sun, X., Weil-Petersson geometry on moduli space of polarized Calabi-Yau manifolds, J. Inst. Math. Jussieu 3 (2004), 185–229. MR 2055709. DOI 10. 1017/S1474748004000076.Google Scholar
[N] Namikawa, Y., Toroidal Compactification of Siegel Spaces, Lecture Notes in Math. 812, Springer, Berlin, 1980. MR 0584625.Google Scholar
[S] Schmid, W., Variation of Hodge structure: The singularities of the period mapping, Invent. Math. 22 (1973), 211–319. MR 0382272.CrossRefGoogle Scholar
[U1] Usui, S., Complex structures on partial compactifications of arithmetic quotients of classifying spaces of Hodge structures, Tohoku Math. J. (2) 47 (1995), 405–429. MR 1344910. DOI 10.2748/tmj/1178225524.Google Scholar
[U2] Usui, S., Generic Torelli theorem for quintic-mirror family, Proc. Japan Acad. Ser. A Math. Sci. 84 (2008), 143–146. MR 2457802.Google Scholar