A new family of counterexamples to the Zariski Cancellation Problem in positive characteristic

TL;DR

This paper constructs an infinite family of higher-dimensional counterexamples to the Zariski Cancellation Problem in positive characteristic, expanding the known set of such counterexamples and demonstrating their distinctness.

Contribution

It introduces a new infinite family of counterexamples in positive characteristic that are non-isomorphic to previous examples, advancing understanding of the Zariski Cancellation Problem.

Findings

Existence of infinitely many non-isomorphic counterexamples in dimension ≥ 3

Counterexamples are distinct from Gupta's family

Counterexamples demonstrate limitations of cancellation in positive characteristic

Abstract

In this paper, over a field of positive characteristic we exhibit an infinite family of counter examples to the Zariski Cancellation Problem in higher dimensions ($\geqslant 3$) which are pairwise non-isomorphic and also non-isomorphic to the existing family of counter examples, demonstrated by Gupta in \cite{adv}.