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VOL. 55 | 2009 Lagrangian fibrations and theta functions
Yuichi Nohara

Editor(s) Jean-Pierre Bourguignon, Motoko Kotani, Yoshiaki Maeda, Nobuyuki Tose

## Abstract

It is known that holomorphic sections of an ample line bundle $L$ (and its tensor power $L^k$) on an Abelian variety $A$ are given by theta functions. Moreover, a natural basis of the space of holomorphic sections is related to a certain Lagrangian fibration of $A$. We study projective embeddings of $A$ given by the basis for $L^k$, and show that moment maps of toric actions on the ambient projective spaces, restricted to $A$, approximate the Lagrangian fibration of $A$ for large $k$. The case of Kummer variety is also discussed.

## Information

Published: 1 January 2009
First available in Project Euclid: 28 November 2018

zbMATH: 1182.53077
MathSciNet: MR2463506

Digital Object Identifier: 10.2969/aspm/05510299