Hyper–Kähler Manifolds of Generalized Kummer Type and the Kuga–Satake Correspondence

We first describe the construction of the Kuga–Satake variety associated to a (polarized) weight-two Hodge structure of hyper-Kähler type. We describe the classical cases where the Kuga–Satake correspondence between a hyper-Kähler manifold and its Kuga–Satake variety has been proved to be algebraic....

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Autores principales: Varesco, M., Voisin, C.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9708794/
https://www.ncbi.nlm.nih.gov/pubmed/36466318
http://dx.doi.org/10.1007/s00032-022-00369-8
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author Varesco, M.
Voisin, C.
author_facet Varesco, M.
Voisin, C.
author_sort Varesco, M.
collection PubMed
description We first describe the construction of the Kuga–Satake variety associated to a (polarized) weight-two Hodge structure of hyper-Kähler type. We describe the classical cases where the Kuga–Satake correspondence between a hyper-Kähler manifold and its Kuga–Satake variety has been proved to be algebraic. We then turn to recent work of O’Grady and Markman which we combine to prove that the Kuga–Satake correspondence is algebraic for projective hyper-Kähler manifolds of generalized Kummer deformation type.
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spelling pubmed-97087942022-12-01 Hyper–Kähler Manifolds of Generalized Kummer Type and the Kuga–Satake Correspondence Varesco, M. Voisin, C. Milan J Math Article We first describe the construction of the Kuga–Satake variety associated to a (polarized) weight-two Hodge structure of hyper-Kähler type. We describe the classical cases where the Kuga–Satake correspondence between a hyper-Kähler manifold and its Kuga–Satake variety has been proved to be algebraic. We then turn to recent work of O’Grady and Markman which we combine to prove that the Kuga–Satake correspondence is algebraic for projective hyper-Kähler manifolds of generalized Kummer deformation type. Springer International Publishing 2022-10-19 2022 /pmc/articles/PMC9708794/ /pubmed/36466318 http://dx.doi.org/10.1007/s00032-022-00369-8 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
Varesco, M.
Voisin, C.
Hyper–Kähler Manifolds of Generalized Kummer Type and the Kuga–Satake Correspondence
title Hyper–Kähler Manifolds of Generalized Kummer Type and the Kuga–Satake Correspondence
title_full Hyper–Kähler Manifolds of Generalized Kummer Type and the Kuga–Satake Correspondence
title_fullStr Hyper–Kähler Manifolds of Generalized Kummer Type and the Kuga–Satake Correspondence
title_full_unstemmed Hyper–Kähler Manifolds of Generalized Kummer Type and the Kuga–Satake Correspondence
title_short Hyper–Kähler Manifolds of Generalized Kummer Type and the Kuga–Satake Correspondence
title_sort hyper–kähler manifolds of generalized kummer type and the kuga–satake correspondence
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9708794/
https://www.ncbi.nlm.nih.gov/pubmed/36466318
http://dx.doi.org/10.1007/s00032-022-00369-8
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