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Projective blowups: a formal and multicentered proof — arXiv:2609.28489

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.28489
License (as archived): CC0-1.0
Archived: 2026-10-08T07:29:04.652Z
SHA-256 of the archived text: 5b4d9daba1d0bbf91819dd0aebb71a54cc72d36d9a5613411752082b4415fc13
Stable URL of this page: https://metraipolis.com/documento/dc_efcf529cefca

How to cite

Projective blowups: a formal and multicentered proof — arXiv:2609.28489 — arXiv (en), https://arxiv.org/abs/2609.28489 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_efcf529cefca (Metraipolis archive dc_efcf529cefca, sha256 5b4d9daba1d0bbf91819dd0aebb71a54cc72d36d9a5613411752082b4415fc13)

BibTeX

@misc{dcefcf529cefca,
  title = {Projective blowups: a formal and multicentered proof — arXiv:2609.28489},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.28489},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_efcf529cefca; sha256 5b4d9daba1d0bbf91819dd0aebb71a54cc72d36d9a5613411752082b4415fc13},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.28489. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We give a machine-checked proof, in Lean 4, of the universal property of multicentered blowups: given a finite family $Z$ of closed subschemes of a scheme $X$, presented on each chart by ideals, there is a scheme $\Bl_Z X$ 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 initial algebra in which a finite family of ideals becomes generated by non-zero-divisors. Existence and uniqueness of the dilatation are established locally, on affine charts, and every subsequent step of the construction, the base change along open immersions, the comparison isomorphisms on overlaps, the triple overlap maps, the cocycle identity, and the independence of the chosen presentation, is deduced from that single local property by uniqueness alone. We give the exact theorem statement as formalized, the proof architecture, and the main new mathematical ingredients, together with the corresponding Lean code.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-25 in cs.LO).
Categorie arXiv: Algebraic Geometry (math.AG) ; Logic in Computer Science (cs.LO).
Pagina del lavoro: https://arxiv.org/abs/2609.28489 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-08T06:44:43.798Z dalla pagina https://arxiv.org/catchup/cs.LO/2026-09-25?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).