the geography of compact irreducible holomorphic symplectic (or hyperkähler) varieties


Hyperkähler manifolds, or irreducible holomorphic symplectic varieties, are important building blocks of objects in complex geometry. Whilst they have amazing properties, their classification is incomplete and only 2 infinite families of deformation types, and 2 sporadic deformation types are known.

This website is dedicated to describing these known types, with the focus being on their properties that are deformation invariant.

More information about hyperkähler varieties is available.

How to contribute?

It is to be expected that there are typos, mistakes, or things that should just be better. If that is the case you can


I would like to thank Thorsten Beckmann, Daniel Huybrechts and Jieao Song for interesting discussions. All remaining mistakes are due to my failures in typing, misinterpreting the literature or (let's hope not!) actual mistakes in the literature.


See pbelmans.ncag.info for ways to contact me. Or just email me at pieterbelmans@gmail.com.