# Examples of irreducible symplectic varieties

## TL;DR

This paper reviews the concept of irreducible symplectic varieties, including their definitions, relationships, and known examples, especially in singular and orbifold contexts, contributing to the understanding of their structure in complex geometry.

## Contribution

It compiles and analyzes various definitions and known examples of irreducible symplectic varieties, especially in singular and orbifold cases, clarifying their interrelations.

## Key findings

- Collected definitions of irreducible symplectic varieties.
- Analyzed relationships among different types.
- Provided a list of known examples.

## Abstract

Irreducible symplectic manifolds are one of the three building blocks of compact K\"ahler manifolds with numerically trivial canonical bundle by the Beauville-Bogomolov decomposition theorem. There are several singular analogues of irreducible symplectic manifolds, in particular in the context of compact K\"ahler orbifolds, and in the context of normal projective varieties with canonical singularities. In this paper we will collect their definitions, analyze their mutual relations and provide a list of known examples.