{"id":"openai-math/Log-abundance-in-numerical-dimension-one-for-threefolds-in-positive-characteristic","pdf":"https://github.com/openai/math/blob/main/preprints/Log-abundance-in-numerical-dimension-one-for-threefolds-in-positive-characteristic-October-5-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Log-abundance-in-numerical-dimension-one-for-threefolds-in-positive-characteristic-October-5-2026","tags":["algebraic-geometry","log-abundance","threefolds","positive-characteristic"],"score":0,"title":"Log abundance in numerical dimension one for threefolds in positive characteristic","domain":"Algebraic and complex geometry","family":"035","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"We prove the numerical-dimension-one case of log abundance for threefolds over algebraically closed fields of characteristic p > 3. If $`(X,B)`$ is a projective log canonical threefold pair with effective rational boundary, and $`K_X+B`$ is ℚ-Cartier, nef, and of numerical dimension one, then $`K_X+B`$ is semiample. Neither terminality nor ℚ-factoriality of X is required.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Log-canonical threefold abundance in numerical dimension one"}