# Fujiki relations and fibrations of irreducible symplectic varieties

## TL;DR

This paper extends key properties of irreducible symplectic manifolds to certain singular varieties, demonstrating that the Beauville-Bogomolov form satisfies Fujiki relations and that these varieties exhibit similar fibration behaviors.

## Contribution

It generalizes Fujiki relations and fibration properties from smooth to singular irreducible symplectic varieties using recent definitions.

## Key findings

- Fujiki relations hold for generalized Beauville-Bogomolov form
- Fibrations of these varieties behave like those of smooth irreducible symplectic manifolds
- The rank of the Beauville-Bogomolov form remains consistent with the smooth case

## Abstract

This paper concerns different types of singular complex projective varieties generalizing irreducible symplectic manifolds. We deduce from known results that the generalized Beauville-Bogomolov form satisfies the Fujiki relations and has the same rank as in the smooth case. This enables us to study fibrations of these varieties; imposing the newer definition from [GKP16, Definition 8.16.2] we show that they behave much like irreducible symplectic manifolds.