English

Dream resolution and principalization II: excellent schemes

Algebraic Geometry 2025-07-22 v2

Abstract

This is the second paper in a project on dream (or memoryless) principalization and resolution methods. It extends this theory from the case of schemes with enough derivations, which was established in [Tem25], to general excellent schemes of characteristic zero. So, similarly to McQuillan's approach developed in [McQ20], the approach of [ATW24] is now extended to the generality of all excellent schemes of characteristic zero. In addition, we precisely describe the set of invariants of canonical centers and establish the resolution in the non-embedded form, where one applies simple (stack-theoretical) modifications along subschemes of a special form that we call tubes. In the regular case these are precisely the subschemes corresponding to canonical centers.

Cite

@article{arxiv.2507.11698,
  title  = {Dream resolution and principalization II: excellent schemes},
  author = {Michael Temkin},
  journal= {arXiv preprint arXiv:2507.11698},
  year   = {2025}
}

Comments

24 pages, a few typos in the first version were corrected, comments are welcome

R2 v1 2026-07-01T04:03:10.389Z