Derived Categories of Hyper-Kähler Manifolds via the LLV Algebra

We mostly review work of Taelman (Derived equivalences of hyperkähler varieties, 2019, arXiv:1906.08081) on derived categories of hyper-Kähler manifolds. We study the LLV algebra using polyvector fields to prove that it is a derived invariant. Applications to the action of derived equivalences on co...

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Autor principal: Beckmann, T.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9708817/
https://www.ncbi.nlm.nih.gov/pubmed/36466317
http://dx.doi.org/10.1007/s00032-022-00358-x
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author Beckmann, T.
author_facet Beckmann, T.
author_sort Beckmann, T.
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description We mostly review work of Taelman (Derived equivalences of hyperkähler varieties, 2019, arXiv:1906.08081) on derived categories of hyper-Kähler manifolds. We study the LLV algebra using polyvector fields to prove that it is a derived invariant. Applications to the action of derived equivalences on cohomology and to the study of their Hodge structures are given.
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spelling pubmed-97088172022-12-01 Derived Categories of Hyper-Kähler Manifolds via the LLV Algebra Beckmann, T. Milan J Math Article We mostly review work of Taelman (Derived equivalences of hyperkähler varieties, 2019, arXiv:1906.08081) on derived categories of hyper-Kähler manifolds. We study the LLV algebra using polyvector fields to prove that it is a derived invariant. Applications to the action of derived equivalences on cohomology and to the study of their Hodge structures are given. Springer International Publishing 2022-06-21 2022 /pmc/articles/PMC9708817/ /pubmed/36466317 http://dx.doi.org/10.1007/s00032-022-00358-x Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Beckmann, T.
Derived Categories of Hyper-Kähler Manifolds via the LLV Algebra
title Derived Categories of Hyper-Kähler Manifolds via the LLV Algebra
title_full Derived Categories of Hyper-Kähler Manifolds via the LLV Algebra
title_fullStr Derived Categories of Hyper-Kähler Manifolds via the LLV Algebra
title_full_unstemmed Derived Categories of Hyper-Kähler Manifolds via the LLV Algebra
title_short Derived Categories of Hyper-Kähler Manifolds via the LLV Algebra
title_sort derived categories of hyper-kähler manifolds via the llv algebra
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9708817/
https://www.ncbi.nlm.nih.gov/pubmed/36466317
http://dx.doi.org/10.1007/s00032-022-00358-x
work_keys_str_mv AT beckmannt derivedcategoriesofhyperkahlermanifoldsviathellvalgebra

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