155 citations · 502 across the 50 of their papers we have counts for
60 papers
On Chern classes of Lagrangian fibered hyper-Kähler manifolds
Claire Voisin
We study the rank stratification for the differential of a Lagrangian fibration over a smooth basis. We also introduce and study the notion of Lagrangian morphism of vector bundles…
Cycle classes on abelian varieties and the geometry of the Abel-Jacobi map
Claire Voisin
We discuss two properties of an abelian variety, namely, being a direct summand in a product of Jacobians and the weaker property of being "split". We relate the first property to…
Geometric representability of 1-cycles on rationally connected threefolds
Claire Voisin
We prove that for any rationally connected threefold , there exists a smooth projective surface and a family of -cycles on parameterized by , inducing an Abel-Jaco…
Computing Riemann-Roch polynomials and classifying hyper-Kähler fourfolds
Olivier Debarre, Daniel Huybrechts, Emanuele Macrì +1
We prove that a hyper-Kähler fourfold satisfying a mild topological assumption is of K3 deformation type. This proves in particular a conjecture of O'Grady stating that hyp…
On fibrations and measures of irrationality of hyper-Kähler manifolds
Claire Voisin
We prove some results on the fibers and images of rational maps from a hyper-Kähler manifold. We study in particular the minimal genus of fibers of a fibration into curves. The las…
Hilbert schemes of K3 surfaces, generalized Kummer, and cobordism classes of hyper-Kähler manifolds
Georg Oberdieck, Jieao Song, Claire Voisin
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 Hilbe…