{"id":"openai-math/Abundance-in-numerical-dimension-one-for-terminal-threefolds-in-positive-characteristic","pdf":"https://github.com/openai/math/blob/main/preprints/Abundance-in-numerical-dimension-one-for-terminal-threefolds-in-positive-characteristic-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Abundance-in-numerical-dimension-one-for-terminal-threefolds-in-positive-characteristic-September-24-2026","tags":["birational-geometry","positive-characteristic","minimal-model-program"],"score":0,"title":"Abundance in numerical dimension one for terminal 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":"Let X be a projective ℚ-factorial terminal threefold over an algebraically closed field of characteristic p > 3. We prove the numerical-dimension-one case of abundance: if K X is nef with $`\\nu(K_X)=1`$, then K X is semiample and $`\\kappa(X,K_X)=1`$.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"Log-canonical threefold abundance in numerical dimension one"}