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Hilbert schemes of K3 surfaces, generalized Kummer, and cobordism classes of hyper-Kähler manifolds

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Bibliographic Details
Main Authors: Oberdieck, Georg (Author) , Song, Jieao (Author) , Voisin, Claire (Author)
Format: Article (Journal)
Language:English
Published: 25 October 2022
In: Pure and applied mathematics quarterly
Year: 2022, Volume: 18, Issue: 4, Pages: 1723-1748
ISSN:1558-8602
DOI:10.4310/PAMQ.2022.v18.n4.a13
Online Access:Resolving-System, lizenzpflichtig, Volltext: https://doi.org/10.4310/PAMQ.2022.v18.n4.a13
Verlag, lizenzpflichtig, Volltext: https://link.intlpress.com/JDetail/1806163600932810754
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Author Notes:Georg Oberdieck, Jieao Song & Claire Voisin
Description
Item Description:Gesehen am 12.12.2024
We prove that the complex cobordism class of any hyper-Kähler manifold of dimension is a unique combination with rational coefficients of classes of products of punctual Hilbert schemes of K3 surfaces. We also prove a similar result using the generalized Kummer varieties instead of punctual Hilbert schemes. As a key step, we establish a closed formula for the top Chern character of their tangent bundles
Special issue celebrating the work of Herb Clemens
Physical Description:Online Resource
ISSN:1558-8602
DOI:10.4310/PAMQ.2022.v18.n4.a13

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