The Bergman Kernel Function. Differentiability at the Boundary.
The class ... is not stable by small deformations.
The complete classification of compactifications of C³ which are projective manifolds with the second Betti number one.
The complex structure on a connected sum of S³ x S³ with trivial canonical bundle.
The Extended Teichmüller Space.
The finiteness of compact varieties in
The Fujiki class and positive degree maps
We show that a map between complex-analytic manifolds, at least one ofwhich is in the Fujiki class, is a biholomorphism under a natural condition on the second cohomologies. We use this to establish that, with mild restrictions, a certain relation of “domination” introduced by Gromov is in fact a partial order.
The geometry of Teichmüller space via geodesic currents.
The graded Lie algebra of a Kähler group.
The growth of regular functions on algebraic sets
We are concerned with the set of all growth exponents of regular functions on an algebraic subset V of . We show that its elements form an increasing sequence of rational numbers and we study the dependence of its structure on the geometric properties of V.
The hodge conjecture for cubic fourfolds
The ideal boundary of a domain in
The moduli and the global period mapping of surfaces with : a counterexample to the global Torelli problem
The moduli of quotients of a compact complex space.
The Monodromy Weight Filtration for a Several Variables Degeneration of Hodge Structures of Weight Two.
The Picard group of a primary Kodaira surface.
The pro-unipotent radical of the pro-algebraic fundamental group of a compact Kähler manifold
The aim of this paper is to study the pro-algebraic fundamental group of a compact Kähler manifold. Following work by Simpson, the structure of this group’s pro-reductive quotient is already well understood. We show that Hodge-theoretic methods can also be used to establish that the pro-unipotent radical is quadratically presented. This generalises both Deligne et al.’s result on the de Rham fundamental group, and Goldman and Millson’s result on deforming representations of Kähler groups, and can...
The rational homotopy theory of smooth, complex projective varieties
The Shafarevich-Tate Conjecture for Pencils of Elliptic Curves on K3 Surfaces.
The Soliton-Ricci Flow with variable volume forms
We introduce a flow of Riemannian metrics and positive volume forms over compact oriented manifolds whose formal limit is a shrinking Ricci soliton. The case of a fixed volume form has been considered in our previouswork.We still call this new flow, the Soliton-Ricci flow. It corresponds to a forward Ricci type flow up to a gauge transformation. This gauge is generated by the gradient of the density of the volumes. The new Soliton-Ricci flow exist for all times. It represents the gradient flow of...