On the $8n^2$-inequality

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173017We give a complete proof of the so called $8n^2$-inequality, a local inequality for the self-intersection of a movable linear system at an isolated centre of a non canonical singularity. The inequality was suggested and several times published by I.Cheltsov but some of his arguments are faulty. We explain the mistake and replace the faulty piece by a correct argument.LaTeX, 8 pagesAlgebraic Geometry14E05; 14E07; 14B05On the $8n^2$-inequalitytext