{"id":"openai-math/Metric-descent-and-rank-preserving-contractions","pdf":"https://github.com/openai/math/blob/main/preprints/Metric-descent-and-rank-preserving-contractions-September-26-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/Metric-descent-and-rank-preserving-contractions-September-26-2026","tags":["complex-geometry","anticanonical-bundle","metrics","algebraic-geometry"],"score":0,"title":"Metric descent and rank-preserving contractions","domain":"Algebraic and complex geometry","family":"068","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"From a smooth semipositive anticanonical metric on a smooth projective complex variety, we construct an unweighted integrable semipositive metric on a corrected anticanonical line of a smooth base, using a normal equidimensional toroidal model and full generic adjoint rank one at exponent zero. The explicit rational boundary correction pulls back to an exceptional divisor. On varieties without positive-degree holomorphic forms, two-metric transfer gives sections with prescribed boundary poles from a finite-volume log-anticanonical metric and a target line with bounded semipositive weights.…","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"}