Toric degenerations in symplectic geometry

Abstract

A toric degeneration in algebraic geometry is a process where a given projective variety is being degenerated into a toric one. Then one can obtain information about the original variety via analyzing the toric one, which is a much easier object to study. Harada and Kaveh described how one incorporates a symplectic structure into this process, providing a very useful tool for solving certain problems in symplectic geometry. Below we present applications of this method to questions about the Gromov width, and cohomological rigidity problems.

This is a conference proceedings paper which gathers results from arXiv:1601.02825 joint with I. Halacheva, arXiv:1607.01163 joint with X. Fang and P. Littelmann, and a project in progress joint with S. Tolman. 20 pages