Hilbert schemes of K3 surfaces, generalized Kummer, and cobordism classes of hyper-Kähler manifolds - Oberdieck, Georg; Song, Jieao; Voisin, Claire (Pure and applied mathematics quarterly, 2022)
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