Thirty-three deformation classes of compact hyperk\"ahler orbifolds
Algebraic Geometry
2026-05-19 v2
Abstract
As their smooth analogue the irreducible symplectic varieties appear as elementary bricks in the generalizations of the Bogomolov decomposition theorem (arXiv:math/0402243, arXiv:2012.00441). Let be a K3 surface; generalizing the Fujiki construction, we investigate the irreducible symplectic varieties with simply connected smooth locus that can be obtained as terminalizations of quotients of the product . In dimension 4, we compute the singularities for 29 orbifolds examples which appear to be independent under deformation. We also provide 4 additional orbifolds examples in dimension 6.
Keywords
Cite
@article{arxiv.2211.14524,
title = {Thirty-three deformation classes of compact hyperk\"ahler orbifolds},
author = {Grégoire Menet},
journal= {arXiv preprint arXiv:2211.14524},
year = {2026}
}
Comments
Final version to appear in Algebra & Number Theory. The computer programs can be found on GitHub or in the first arxiv version of the paper