Lagrangian fibrations and theta functions

Details Lagrangian fibrations and theta functions Lagrangian fibrations and theta functions

2006-04-14

arxiv.org/abs/math/0604330v1

Mathematics

Differential Geometry

64 pages

Scientific paper

In this thesis we study asymptotic behavior of projective embeddings of abelian varieties and their amoebas. The projective embeddings are given by theta functions. It is known that a Lagrangian fibration of the abelian variety determines a basis of theta functions. After reviewing the relation from the viewpoint of geometric quantization and mirror symmetry, we prove that the Lagrangian fibration of the abelian variety can be approximated by the moment maps of natural torus action in a suitable sense. In the final section we discuss a part of the result in more general setting.

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