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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Detalles Bibliográficos
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
Descripción
Sumario: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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