Chern degree functions
We introduce Chern degree functions for complexes of coherent sheaves on a polarized surface, which encode information given by stability conditions on the boundary of the $(\alpha, \beta)$-plane. We prove that these functions extend to continuous real valued functions and we study their differentia...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/194429 |
| Acceso en línea: | https://hdl.handle.net/2445/194429 |
| Access Level: | acceso abierto |
| Palabra clave: | Homologia Geometria algebraica Superfícies algebraiques Àlgebra homològica Categories (Matemàtica) Homology Algebraic geometry Algebraic surfaces Homological algebra Categories (Mathematics) |
| Sumario: | We introduce Chern degree functions for complexes of coherent sheaves on a polarized surface, which encode information given by stability conditions on the boundary of the $(\alpha, \beta)$-plane. We prove that these functions extend to continuous real valued functions and we study their differentiability in terms of stability. For abelian surfaces, Chern degree functions coincide with the cohomological rank functions defined by Jiang-Pareschi. We illustrate in some geometrical situations a general strategy to compute these functions. |
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