{"id":"openai-math/Integrability-of-split-tangent-bundles-on-rationally-connected-manifolds","pdf":"https://github.com/openai/math/blob/main/preprints/Integrability-of-split-tangent-bundles-on-rationally-connected-manifolds-September-23-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/Integrability-of-split-tangent-bundles-on-rationally-connected-manifolds-September-23-2026","tags":["algebraic-geometry","complex-geometry","rationally-connected"],"score":0,"title":"Integrability of split tangent bundles on rationally connected manifolds","domain":"Algebraic and complex geometry","family":"052","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"We prove that both summands of every specified holomorphic splitting of the tangent bundle of a smooth rationally connected projective complex manifold into two positive-rank subbundles are integrable. This proves Höring's conjecture on rationally connected projective manifolds. Höring's product theorem then gives a product decomposition compatible with the specified splitting.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"Tangent splittings and product decompositions"}