The Classification Machines: Birational Geometry's Big Programme

Deep End Era. Engineering with Sankalp · Oct 12, 2026 · 46m

Part 12 of "The Machine's Theorems", a lighter episode. Farah and Augustin use a refinery's pig-cleaning campaign and a sculptor's chisel to explain birational geometry: canonical divisors, contractions, flips, termination and abundance. We then read OpenAI's manuscripts on termination for fourfolds (family 056, including six Kähler manuscripts revised on 7 October), log abundance in every dimension (034) and in positive characteristic (035), Fujita's freeness conjecture (038), Nagata's conjecture (039, Lean-listed), P = W for fixed determinant (043) and a counterexample to Griffiths'…