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...

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Detalles Bibliográficos
Autores: Lahoz Vilalta, Martí, Rojas, Andrés
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)
Descripción
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.