Mathematische Annalen

, Volume 333, Issue 4, pp 741–757

Projective Embeddings and Lagrangian Fibrations of Abelian Varieties


DOI: 10.1007/s00208-005-0685-8

Cite this article as:
Nohara, Y. Math. Ann. (2005) 333: 741. doi:10.1007/s00208-005-0685-8


It is well known that every Abelian variety can be embedded into projective spaces by theta functions and the basis of theta functions are determined by choosing a Lagrangian fibration. In this paper, we prove that the restriction of natural Lagrangian fibrations (moment maps) of projective spaces converge to that of the Abelian variety in ``the Gromov-Hausdorff topology''. This is, in some sense, a Lagrangian fibration version of the convergence theorem of G. Tian [6] and S. Zelditch [7] for Kähler metrics.

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© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Graduate School of MathematicsNagoya UniversityChikusa-kuJapan