Regular pullback of generalized cluster structures
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914390303834112 |
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| author | Gekhtman, Misha Shapiro, Michael Vainshtein, Alek |
| author_facet | Gekhtman, Misha Shapiro, Michael Vainshtein, Alek |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12496 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Regular pullback of generalized cluster structures Gekhtman, Misha Shapiro, Michael Vainshtein, Alek Commutative Algebra Algebraic Geometry 13F60 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. |
| title | Regular pullback of generalized cluster structures |
| topic | Commutative Algebra Algebraic Geometry 13F60 |
| url | https://arxiv.org/abs/2603.12496 |