{"id":"openai-math/A-projective-fourfold-with-large-fundamental-group-and-non-Stein-universal-cover","pdf":"https://github.com/openai/math/blob/main/preprints/A-projective-fourfold-with-large-fundamental-group-and-non-Stein-universal-cover-October-5-2026/large-fundamental-group-non-stein.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-projective-fourfold-with-large-fundamental-group-and-non-Stein-universal-cover-October-5-2026","tags":["algebraic-geometry","complex-geometry","fundamental-group"],"score":0,"title":"A projective fourfold with large fundamental group and non-Stein universal cover","domain":"Algebraic and complex geometry","family":"046","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"We construct a smooth projective complex fourfold with large fundamental group whose universal cover is not Stein. The universal cover contains no positive-dimensional compact complex-analytic subvariety, so this disproves Shafarevich's holomorphic-convexity conjecture even under the large-fundamental-group hypothesis.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Shafarevich counterexamples in dimension two and with large fundamental group"}