Some terminal orders on 3-folds

Daniel Chan; Colin Ingalls

Some terminal orders on 3-folds

Algebraic Geometry 2026-07-03 v1 Rings and Algebras

Authors: Daniel Chan , Colin Ingalls

Abstract

We produce the first known examples of non-trivial terminal local orders in the 3-dimensional case. We exhibit two different constructions. The first produces maximal orders with given toric ramification data. Since toric terminal ramification data in dimension 3 has been classified this produces toric examples. The second construction yields maximal orders ramified on surfaces with Kleinian singularities. These are automatically terminal.

Keywords

terminal orders 3-folds toric ramification Kleinian singularities maximal orders

Cite

@article{arxiv.2607.02950,
  title  = {Some terminal orders on 3-folds},
  author = {Daniel Chan and Colin Ingalls},
  journal= {arXiv preprint arXiv:2607.02950},
  year   = {2026}
}