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Article Dans Une Revue Pure and Applied Mathematics Quarterly Année : 2022

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

Résumé

We prove that the complex cobordism class of any hyper-Kähler manifold of dimension 2n 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.
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Dates et versions

hal-03403464 , version 1 (26-10-2021)
hal-03403464 , version 2 (10-10-2022)

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  • HAL Id : hal-03403464 , version 2

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Georg Oberdieck, Jieao Song, Claire Voisin. Hilbert schemes of K3 surfaces, generalized Kummer, and cobordism classes of hyper-Kähler manifolds. Pure and Applied Mathematics Quarterly, In press. ⟨hal-03403464v2⟩
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