{"id":"openai-math/A-surface-counterexample-to-Shafarevich-holomorphic-convexity","pdf":"https://github.com/openai/math/blob/main/preprints/A-surface-counterexample-to-Shafarevich-holomorphic-convexity-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-surface-counterexample-to-Shafarevich-holomorphic-convexity-September-23-2026","tags":["complex-geometry","algebraic-surfaces","holomorphic-convexity"],"score":0,"title":"A surface counterexample to Shafarevich holomorphic convexity","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 connected projective complex surface whose universal cover is not holomorphically convex. This disproves the Shafarevich conjecture on holomorphic convexity in complex dimension two.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"Shafarevich counterexamples in dimension two and with large fundamental group"}