Schemes of modules over gentle algebras and laminations of surfaces
| Autor: | Jan Schröer, Christof Geiß, Daniel Labardini-Fragoso |
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| Rok vydání: | 2020 |
| Předmět: |
Surface (mathematics)
Pure mathematics General Mathematics General Physics and Astronomy Special class Computer Science::Digital Libraries Cluster algebra Set (abstract data type) symbols.namesake Jacobian matrix and determinant Bijection symbols FOS: Mathematics Affine transformation Representation Theory (math.RT) Mathematics::Representation Theory Mathematics - Representation Theory Mathematics |
| DOI: | 10.48550/arxiv.2005.01073 |
| Popis: | We study the affine schemes of modules over gentle algebras. We describe the smooth points of these schemes, and we also analyze their irreducible components in detail. Several of our results generalize formerly known results, e.g. by dropping acyclicity, and by incorporating band modules. A special class of gentle algebras are Jacobian algebras arising from triangulations of unpunctured marked surfaces. For these we obtain a bijection between the set of generically tau-reduced decorated irreducible components and the set of laminations of the surface. As an application, we get that the set of bangle functions (defined by Musiker-Schiffler-Williams) in the upper cluster algebra associated with the surface coincides with the set of generic Caldero-Chapoton functions. Comment: 68 pages. Changes v2: Section 3 is new. We fixed a few typos and added 2 references. v3: Final version with a few improvements suggested by a referee. To appear in Selecta Math. Use PDF-LaTeX for correct display of colored diagrams |
| Databáze: | OpenAIRE |
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