# Toric degenerations in symplectic geometry

## TL;DR

This paper discusses the use of toric degenerations in symplectic geometry to analyze complex varieties by degenerating them into simpler toric varieties, enabling new insights into symplectic invariants and rigidity problems.

## Contribution

It introduces a method combining toric degenerations with symplectic structures, applied to solve problems like Gromov width and cohomological rigidity.

## Key findings

- Applied to Gromov width estimation
- Addressed cohomological rigidity issues
- Enhanced understanding of symplectic invariants

## 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.