{"id":"openai-math/A-conditional-abelianity-theorem-for-special-fourfold-pairs-with-a-half-weight-divisor","pdf":"https://github.com/openai/math/blob/main/preprints/A-conditional-abelianity-theorem-for-special-fourfold-pairs-with-a-half-weight-divisor-October-5-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-conditional-abelianity-theorem-for-special-fourfold-pairs-with-a-half-weight-divisor-October-5-2026","tags":["algebraic-geometry","kahler-manifolds","fundamental-groups","orbifolds"],"score":0,"title":"A conditional abelianity theorem for special fourfold pairs with a half-weight divisor","domain":"Algebraic and complex geometry","family":"057","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Fundamental groups of special complex varieties and root orbifolds"}