Regular pullback of generalized cluster structures
Commutative Algebra
2026-03-16 v1 Algebraic Geometry
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.
Cite
@article{arxiv.2603.12496,
title = {Regular pullback of generalized cluster structures},
author = {Misha Gekhtman and Michael Shapiro and Alek Vainshtein},
journal= {arXiv preprint arXiv:2603.12496},
year = {2026}
}