{"id":"openai-math/Universal-cover-splitting-for-compact-Kahler-manifolds","pdf":"https://github.com/openai/math/blob/main/preprints/Universal-cover-splitting-for-compact-Kahler-manifolds-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Universal-cover-splitting-for-compact-Kahler-manifolds-September-23-2026","tags":["complex-geometry","kahler-manifolds","holomorphic-bundles","differential-geometry"],"score":0,"title":"Universal-cover splitting for compact Kähler manifolds","domain":"Algebraic and complex geometry","family":"052","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"We prove the two-summand form of Beauville's compatible splitting conjecture. If the tangent bundle of a compact connected Kähler manifold decomposes into two integrable holomorphic subbundles of positive rank, then its ordinary universal cover admits a product decomposition whose factor tangent bundles are the lifted specified summands.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":true,"family_title":"Tangent splittings and product decompositions"}