Regular pullback of generalized cluster structures

Misha Gekhtman; Michael Shapiro; Alek Vainshtein

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arXiv · 2603.12496

Regular pullback of generalized cluster structures

Misha Gekhtman·Michael Shapiro·Alek Vainshtein

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Abstract

We consider the problem of lifting a regular cluster structure on a quasi-affine variety to the ambient affine space and a similar problem of defining a regular pullback of a regular cluster structure under a dominant rational map between affine spaces. We provide sufficient conditions for the existence of the corresponding object, called an almost-cluster structure, study its combinatorics, compatible Poisson bracket and the corresponding upper cluster algebra.

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Misha Gekhtman, Michael Shapiro, Alek Vainshtein. 2026-03-12. Regular pullback of generalized cluster structures. https://arxiv.org/abs/2603.12496

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