{"id":"hexagon/2610.00447","pdf":"https://hexagonmath.org/pdf/2610.00447v1","url":"https://hexagonmath.org/abs/2610.00447v1","tags":["msc:14J60"],"score":0,"title":"Point Separation for Adjoint Line Bundles","domain":"math.AG","origin":"ai-generated","source":"hexagon","authors":["Brian Nugent"],"reviews":0,"subject":"math.AG","summary":"Let X be a smooth complex projective variety of dimension n and let L be an ample line bundle. Using the freeness and minimization inputs specified in the introduction, we prove that KX + mL separates distinct points for every integer m ≥ n + 2, the sharp bound predicted by Fujita’s very ampleness conjecture. Exponential-moment convergence produces point-centred minimizing valuations at both points in a common degree. Strict convexity then gives a divisor with discrepancy equality at one point and strict excess at the other. A rational perturbation on a resolution, followed by…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-22","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}