Projective Embeddings and Lagrangian Fibrations of Abelian Varieties
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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  and S. Zelditch  for Kähler metrics.
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