Non-cancellative varieties, maximal tori, and the Makar-Limanov invariant

Sergey Gaifullin; Mikhail Petrov

Non-cancellative varieties, maximal tori, and the Makar-Limanov invariant

Algebraic Geometry 2026-07-15 v1

Authors: Sergey Gaifullin , Mikhail Petrov

Abstract

In this paper, we construct a wide class of new counterexamples to the generalized Zariski cancellation problem. The cylinders over these counterexamples have infinitely many non-conjugate maximal tori in their regular automorphism groups. We provide an example of a variety with maximal tori of different dimensions in its automorphism group. Additionally, we prove that a cylinder over a non-rigid trinomial variety without a line factor is generically flexible, and hence, has a trivial Makar-Limanov invariant.

Keywords

Zariski cancellation problem maximal tori Makar-Limanov invariant flexible varieties trinomial varieties automorphism groups

Cite

@article{arxiv.2607.13593,
  title  = {Non-cancellative varieties, maximal tori, and the Makar-Limanov invariant},
  author = {Sergey Gaifullin and Mikhail Petrov},
  journal= {arXiv preprint arXiv:2607.13593},
  year   = {2026}
}