Stability conditions in families
We develop a theory of Bridgeland stability conditions and moduli spaces of semistable objects for a family of varieties. Our approach is based on and generalizes previous work by Abramovich-Polishchuk, Kuznetsov, Lieblich, and Piyaratne-Toda. Our notion includes openness of stability, semistable re...
| Autores: | , , , , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/194431 |
| Acceso en línea: | https://hdl.handle.net/2445/194431 |
| Access Level: | acceso abierto |
| Palabra clave: | Geometria algebraica Homologia Categories (Matemàtica) Varietats simplèctiques Algebraic geometry Homology Categories (Mathematics) Symplectic manifolds |
| id |
ES_e649dcd53ae5b89e9ec775e032e5bc50 |
|---|---|
| oai_identifier_str |
oai:recercat.cat:2445/194431 |
| network_acronym_str |
ES |
| network_name_str |
España |
| repository_id_str |
|
| spelling |
Stability conditions in familiesLahoz Vilalta, MartíBayer, ArendMacrì, EmanuelNuer, HowardPerry, AlexanderStellari, PaoloGeometria algebraicaHomologiaCategories (Matemàtica)Varietats simplèctiquesAlgebraic geometryHomologyCategories (Mathematics)Symplectic manifoldsWe develop a theory of Bridgeland stability conditions and moduli spaces of semistable objects for a family of varieties. Our approach is based on and generalizes previous work by Abramovich-Polishchuk, Kuznetsov, Lieblich, and Piyaratne-Toda. Our notion includes openness of stability, semistable reduction, a support property uniformly across the family, and boundedness of semistable objects. We show that such a structure exists whenever stability conditions are known to exist on the fibers. Our main application is the generalization of Mukai's theory for moduli spaces of semistable sheaves on K3 surfaces to moduli spaces of Bridgeland semistable objects in the Kuznetsov component associated to a cubic fourfold. This leads to the extension of theorems by Addington-Thomas and Huybrechts on the derived category of special cubic fourfolds, to a new proof of the integral Hodge conjecture, and to the construction of an infinite series of unirational locally complete families of polarized hyperkähler manifolds of K3 type. Other applications include the deformation-invariance of Donaldson-Thomas invariants counting Bridgeland stable objects on Calabi-Yau threefolds, and a method for constructing stability conditions on threefolds via degeneration.Springer2023202320212023info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion169 p.application/pdfapplication/pdfhttps://hdl.handle.net/2445/194431Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésReproducció del document publicat a: https://doi.org/10.1007/s10240-021-00124-6Publications mathématiques de l'IHÉS, 2021, num. 133, p. 157-325https://doi.org/10.1007/s10240-021-00124-6cc by (c) Arend Bayer et al., 2021http://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccessoai:recercat.cat:2445/1944312026-05-29T05:05:01Z |
| dc.title.none.fl_str_mv |
Stability conditions in families |
| title |
Stability conditions in families |
| spellingShingle |
Stability conditions in families Lahoz Vilalta, Martí Geometria algebraica Homologia Categories (Matemàtica) Varietats simplèctiques Algebraic geometry Homology Categories (Mathematics) Symplectic manifolds |
| title_short |
Stability conditions in families |
| title_full |
Stability conditions in families |
| title_fullStr |
Stability conditions in families |
| title_full_unstemmed |
Stability conditions in families |
| title_sort |
Stability conditions in families |
| dc.creator.none.fl_str_mv |
Lahoz Vilalta, Martí Bayer, Arend Macrì, Emanuel Nuer, Howard Perry, Alexander Stellari, Paolo |
| author |
Lahoz Vilalta, Martí |
| author_facet |
Lahoz Vilalta, Martí Bayer, Arend Macrì, Emanuel Nuer, Howard Perry, Alexander Stellari, Paolo |
| author_role |
author |
| author2 |
Bayer, Arend Macrì, Emanuel Nuer, Howard Perry, Alexander Stellari, Paolo |
| author2_role |
author author author author author |
| dc.subject.none.fl_str_mv |
Geometria algebraica Homologia Categories (Matemàtica) Varietats simplèctiques Algebraic geometry Homology Categories (Mathematics) Symplectic manifolds |
| topic |
Geometria algebraica Homologia Categories (Matemàtica) Varietats simplèctiques Algebraic geometry Homology Categories (Mathematics) Symplectic manifolds |
| description |
We develop a theory of Bridgeland stability conditions and moduli spaces of semistable objects for a family of varieties. Our approach is based on and generalizes previous work by Abramovich-Polishchuk, Kuznetsov, Lieblich, and Piyaratne-Toda. Our notion includes openness of stability, semistable reduction, a support property uniformly across the family, and boundedness of semistable objects. We show that such a structure exists whenever stability conditions are known to exist on the fibers. Our main application is the generalization of Mukai's theory for moduli spaces of semistable sheaves on K3 surfaces to moduli spaces of Bridgeland semistable objects in the Kuznetsov component associated to a cubic fourfold. This leads to the extension of theorems by Addington-Thomas and Huybrechts on the derived category of special cubic fourfolds, to a new proof of the integral Hodge conjecture, and to the construction of an infinite series of unirational locally complete families of polarized hyperkähler manifolds of K3 type. Other applications include the deformation-invariance of Donaldson-Thomas invariants counting Bridgeland stable objects on Calabi-Yau threefolds, and a method for constructing stability conditions on threefolds via degeneration. |
| publishDate |
2021 |
| dc.date.none.fl_str_mv |
2021 2023 2023 2023 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
| format |
article |
| status_str |
publishedVersion |
| dc.identifier.none.fl_str_mv |
https://hdl.handle.net/2445/194431 |
| url |
https://hdl.handle.net/2445/194431 |
| dc.language.none.fl_str_mv |
Inglés |
| language_invalid_str_mv |
Inglés |
| dc.relation.none.fl_str_mv |
Reproducció del document publicat a: https://doi.org/10.1007/s10240-021-00124-6 Publications mathématiques de l'IHÉS, 2021, num. 133, p. 157-325 https://doi.org/10.1007/s10240-021-00124-6 |
| dc.rights.none.fl_str_mv |
cc by (c) Arend Bayer et al., 2021 http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess |
| rights_invalid_str_mv |
cc by (c) Arend Bayer et al., 2021 http://creativecommons.org/licenses/by/3.0/es/ |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
169 p. application/pdf application/pdf |
| dc.publisher.none.fl_str_mv |
Springer |
| publisher.none.fl_str_mv |
Springer |
| dc.source.none.fl_str_mv |
Articles publicats en revistes (Matemàtiques i Informàtica) reponame:Recercat. Dipósit de la Recerca de Catalunya instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| instname_str |
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| reponame_str |
Recercat. Dipósit de la Recerca de Catalunya |
| collection |
Recercat. Dipósit de la Recerca de Catalunya |
| repository.name.fl_str_mv |
|
| repository.mail.fl_str_mv |
|
| _version_ |
1869422753263648768 |
| score |
15,81155 |