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arXiv · 2607.13593

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

Sergey Gaifullin·Mikhail Petrov
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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.

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Sergey Gaifullin, Mikhail Petrov. 2026-07-15. Non-cancellative varieties, maximal tori, and the Makar-Limanov invariant. https://arxiv.org/abs/2607.13593

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