arXiv:2609.28489 · v2

Projective blowups: a formal and multicentered proof

首次提交 2026-08-13 15:43

版本更新 2026-11-05 02:28

雷达观测 2026-11-05 12:12

摘要

We give a machine-checked proof, in Lean 4, of the universal property of multi- centered blowups: given a finite family Z of closed subschemes of a scheme X, presented on each chart by ideals, there is a scheme BlZ X over X, terminal among X-schemes on which every member of the family becomes an effective Cartier divisor. To the best of our knowledge this is the first formalisation of blowups, single- or multicentered, in any theorem prover. The proof is organised around the universal property of the multicentered dilatation of a ring. The comparison isomorphisms on overlaps, the cocycle identity, and the independence of the chosen presentation are obtained from the uniqueness part of this universal property. We give the exact theorem statement as formalized, the proof architecture, and the main new mathematical ingredients, together with the corresponding Lean code.