Formalizing multi-centered dilatations of schemes and their application to deformation spaces in Lean 4

We report on a formalization in Lean 4 of multi-centered dilatations of schemes
[26] and of the multi-centered deformation spaces of [13]. It covers the ringlevel
theory and its globalization to schemes: the tower formula, reindexing, the
monopoly isomorphism, functoriality, base change, iterated dilatations, and ŸŸ4
5 of [26]. Using the multi-graded Proj schemes of [27], we prove that a dilatation is
an open subscheme of the multi-centered blowup of its centers. Moreover we formalize
the deformation spaces of [13], their panels, and the panelization theorem
[13, Thm. 3.7], at ring and scheme level. Where [26] works with algebraic spaces
and étale coverings, we work with schemes and Zariski open immersions throughout.
The development is about 22 550 lines; every stated result is proved without
sorry and on the three standard axioms of Lean's classical foundation. Source:
https://github.com/rndmx/SchDil.