Mathematische Annalen

, Volume 333, Issue 4, pp 741–757 | Cite as

Projective Embeddings and Lagrangian Fibrations of Abelian Varieties

  • Yuichi NoharaEmail author


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.


Projective Space Convergence Theorem Theta Function Abelian Variety Projective Embedding 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Graduate School of MathematicsNagoya UniversityChikusa-kuJapan

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