{"id":"openai-math/Integrable-metrics-and-effectivity-with-controlled-boundary","pdf":"https://github.com/openai/math/blob/main/preprints/Integrable-metrics-and-effectivity-with-controlled-boundary-September-26-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/Integrable-metrics-and-effectivity-with-controlled-boundary-September-26-2026","tags":["algebraic-geometry","effective-divisors","complex-geometry"],"score":0,"title":"Integrable metrics and effectivity with controlled boundary","domain":"Algebraic and complex geometry","family":"068","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"Let Y be smooth projective and let C be an effective integral divisor. If $`-K_Y+C`$ admits a metric with a global strict curvature lower bound for which the canonical section of C is locally square integrable, every pseudoeffective rational divisor becomes rationally effective after an effective correction supported on C . For a smooth projective X with smoothly semipositive $`L=-K_X`$, sections of $`m_jL-P`$ at unbounded positive exponents, with any fixed pseudoeffective Cartier error P , yield a section of a positive multiple of L .","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-26","reactions":{},"formalized":false,"family_title":"Anticanonical nonvanishing in every dimension"}