Level 3: A conditional abelianity theorem for special fourfold pairs with a half-weight divisor

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LEVEL 3 OF 3 · Campana's abelianity conjecture and special varieties

A conditional abelianity theorem for special fourfold pairs with a half-weight divisor

expertly designed by an internal OpenAI model · released 2026-10-05 · original PDF

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How to play: Using the abelianity theorem for special compact Kähler manifolds in every dimension, we prove virtual abelianity of the entire orbifold fundamental group of the special order-two root orbifold associated with a pair $(X,\tfrac12D)$, where X is a smooth projective fourfold and D is a nonempty smooth connected divisor. We construct a special smooth projective eightfold whose fundamental group surjects onto the required group.

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