Calculation of Rozansky-Witten invariants on the Hilbert schemes of points on a K3 surface and the generalised kummer varieties.
Canonical metrics on some domains of
The study of the existence and uniqueness of a preferred Kähler metric on a given complex manifold is a very important area of research. In this talk we recall the main results and open questions for the most important canonical metrics (Einstein, constant scalar curvature, extremal, Kähler-Ricci solitons) in the compact and the non-compact case, then we consider a particular class of complex domains in , the so-called Hartogs domains, which can be equipped with a natural Kaehler metric ....
Classical Poincaré metric pulled back off singularities using a Chow-type theorem and desingularization
We construct complete Kähler metrics on the nonsingular set of a subvariety of a compact Kähler manifold. To that end, we develop (i) a constructive method for replacing a sequence of blow-ups along smooth centers, with a single blow-up along a product of coherent ideals corresponding to the centers and (ii) an explicit local formula for a Chern form associated to this ‘singular’ blow-up. Our metrics have a particularly simple local formula of a sum of the original metric and of the pull back...
Compact lcK manifolds with parallel vector fields
We show that for n > 2 a compact locally conformally Kähler manifold (M2n , g, J) carrying a nontrivial parallel vector field is either Vaisman, or globally conformally Kähler, determined in an explicit way by a compact Kähler manifold of dimension 2n − 2 and a real function.
Connexité abélienne des variétés kählériennes compactes
Construction of Kähler surfaces with constant scalar curvature
Convergence in capacity on smooth hypersurfaces of compact Kähler manifolds
We study restrictions of ω-plurisubharmonic functions to a smooth hypersurface S in a compact Kähler manifold X. The result obtained and the characterization of convergence in capacity due to S. Dinew and P. H. Hiep [to appear in Ann. Scuola Norm. Sup. Pisa Cl. Sci.] are used to study convergence in capacity on S.
Covariant Cauchy-Riemann operators and higher Laplacians on Kähler manifolds.
Curvature properties of the Calabi-Yau moduli.