Abstract
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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and estimates of the Bergman kernel. J. Funct. Anal. 182(2), 390–426 (2001)Author information
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Nohara, Y. Projective Embeddings and Lagrangian Fibrations of Abelian Varieties. Math. Ann. 333, 741–757 (2005). https://doi.org/10.1007/s00208-005-0685-8
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DOI: https://doi.org/10.1007/s00208-005-0685-8