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Abelianity Conjecture

The abelianity conjecture for special compact Kähler manifolds asserts that their fundamental groups are virtually Abelian. This means that the entire discrete group contains an Abelian subgroup of finite index, equivalently that the manifold has a connected finite unramified holomorphic cover with Abelian fundamental group.

A class-2 nilpotent group has all commutators central.

See also

Bogomolov Sheaf, Fundamental Group, Group Representation, Kaehler Manifold, Nilpotent Group, Orbifold Fundamental Group, Special Variety

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References

Campana, F. and Claudon, B. "Abelianity Conjecture for Special Compact Kähler 3-Folds." Proc. Edinb. Math. Soc. 57, 55-78, 2014. https://doi.org/10.1017/S0013091513000849.Cao, J.; Deng, Y.; Hacon, C. D.; and Păun, M. "Two-Step Nilpotent Monodromy of Local Systems on Special Varieties." 7 Apr 2026. https://arxiv.org/abs/2603.14539v2.

Cite this as:

Weisstein, Eric W. "Abelianity Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AbelianityConjecture.html

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