Lagrangian fibrations and theta functions
Yuichi Nohara
Abstract
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.
Create a lesson
Related papers
A note on the BRST-BV Formalism Explanation of Deformation Quantization and Algebraic Index Theorem
Lihao Zhao
Biharmonic submanifolds in nonpositive space forms
Yu Fu, Min-chun Hong, Dan Yang
Conjugate radius and parabolicity along the Ricci flow
Chandan Kumar Mondal
Pure Spinor Factorization of Belinski-Zakharov Solitons and Regular Gravitational Instantons
Steffen Aksteiner
Flexibility of Laplace-Beltrami eigenfunctions under metric variation
Andrei Agrachev, Nicola Da Ponte, Antonio Lerario et al.
C1-rigidity of Hp,q-convex cocompact representations of Gromov hyperbolic groups
Nikolay Bogachev