Calculation of Rozansky-Witten invariants on the Hilbert schemes of points on a K3 surface and the generalised kummer varieties.
Compatible complex structures on twistor space
Let be a Riemannian 4-manifold. The associated twistor space is a bundle whose total space admits a natural metric. The aim of this article is to study properties of complex structures on which are compatible with the fibration and the metric. The results obtained enable us to translate some metric properties on (scalar flat, scalar-flat Kähler...) in terms of complex properties of its twistor space .
Connections with the tensor property associated with a quaternionic projective transformation. (Connexions ayant la propriété tensorielle associées à une transformation projectif quaternionique.)
Curvature of hyperkähler quotients
We prove estimates for the sectional curvature of hyperkähler quotients and give applications to moduli spaces of solutions to Nahm’s equations and Hitchin’s equations.